As a teenager, if i I could have looked in the future and discover I'd be studying algebra/math as a senior (60 year old) for FUN I'd think I'd lost my mind😂❤❤❤
For sure!!!!!!! It’s SO reassuring to recall/relearn it through this very patient teachers guidance! It’s bothered me that I’ve not used it and therefore have lost it, so yes! It IS. both fun and cognitively reassuring to do it once again here!
I enjoy your classes. In 1959 I was in hospital for 6 weeks and home for 6 weeks, back in junior math without ever opening a book, I was the only one in the class that could solve homework.Then in 2013 I had chemo and radiation and had to start using a calculator for other than trig functions. Watching your classes some of it comes back. Thank you
Thank you for offering this here!!! I am part of the 60+ club here! ✨🎉😅 It’s SO reassuring to recall/relearn it through this very patient teachers guidance! It’s bothered me that I’ve not used it and therefore have lost it, so yes! It IS. both fun and cognitively reassuring to do it once again here! You are indeed doing a great service to many, kind sir! Again, thank you!
LOL - 60 is just right around the corner for me. (Where did the time go??) I was not crazy about math in high school as it seemed like they always went too fast. I liked my math teachers, though, I just had trouble keeping up. In college, I began to like it a bit more as made more sense the second time around - and I only had math classes every other day. Now it has become an enjoyable of a hobby for me next to collecting classical music CD's. BTW, one of my former math teachers, dear old Mr. Robert Parks passed away one year ago this month (in January 2023) at the age of 93 - may he rest in eternal peace!!
As an engineering student it was seldom the calculus that gave me problems, it was the algebra that gave me fits because it was so far back in my education that I was out of practice. Practice and repetition keep the skills fresh.
True. When I started my engineering education I signed up for Trigonometry and found out I forgot Algebra from high school even though I got A's. So I dropped out and took College Algebra. Long story short I finished all the math requirements with A's and graduated with B. S. in Mechanical Engineering PI TAU SIGMA the International Honor Society for Mechanical Engineers.
As an engineer, I worked it out *numerically* by trial and error starting at 2^Pi (just for fun), and adding decimal digits and got 2^3.1699250014425 = 9.
My wife does word puzzles to try to stay sharp. She is 70. I am 72 and trying to stay sharp doing and re-learning math. My 11 yr old granddaughter helped me get started by asking me to help her with her 6th grade math. 😅
I am of a similar age and I have on occasions tried to help the younger generation (including my daughters) with their maths problems and mostly gave up because the current method of teaching is so vague as to be incomprehensible and to me defies logic. One attempt was to solve a problem for a colleagues daughter, where I built up the answer from the information given. The working out was to me at a higher level than I thought was appropriate for his daughter's age. A couple of days later I was informed that the pupils were not to work the answer out but to guess it! Whilst its obvious that through life you estimate what answers might be so that you can validate the actual solution but to just simply guess the answer to a question does not bode well for the human race. Imagine if NASA guessed all the manoeuvre inputs for a trip to the Moon!
there is no scientific evidence to prove word puzzles prevent dementia, and other issues. More so there is evidence that healthy eating, and exercise prevents all age related issues.
JOY and DANCING FEET! I rose to the challenge and recalled the solution method from high school math before I had to resort to watching the video. I'm 64, so it has been a while since I needed to do this kind of math. A small thing, but it made my day. A similar event happened when my high school son came up to me and asked how to solve a calculus problem 20 years ago.
Must of done this 30-40 years ago and completely forgotten because I've never needed to use it. Quite satisfying that it came back when explained, I'll be watching more.
I would use logarithms for this: 2^x = 9 log of both sides log(2^x) = log(9) x log(2) = log(9) x = log(9)/log(2) Of course you need log tables to get the solution. Maybe there's another way. But since 2^3 = 8 and 2^4 = 16, we know the answer will be somewhere between 3 and e4.
Its 55 years since I first learned this material and now I have almost completely forgotten it. We had Log Books back then, calculations were slower and calculators were only just emerging. I never used manual algebra or calculus in my working life as computer programs took care of multiple data streams and operations almost instantly. Now, I'm relearning the fundamentals solely to keep my mind active. Thanks for your explanations and patience.
Dad, an engineer, bought himself a Texas Instruments model and in 1974 he bought me a Colex. It was the first calculator in my year group but we still had to know how to use log books and slide rules well before and well after 1974! @@mariondavis5735
Great!! I went through Calculus III and Differential Equations many years ago and nobody explained to me like this what a log is. Thanks. I'm thinking of studying Math again to learn all that I forgot.
I actually enjoyed this lesson.I'm retired and just when I thought that I no longer had use for this stuff, I just found out how wrong I was.I think I just found something that I cam actually gravitate to.Keep the wheels in the old brain turning. Thank you so much. Keep up the good work.
I think it's the story about wisdom. When we're old we can actually see the usefulness of things we deemed as useless as kids. I ruminate over this thought every time I use algebra. It also might be a good idea if teachers would employ mathematics to real life situations.
Thank you for explaining it so clear. In the Netherlands I learned about exponential equations and logarithms at school long ago. Thank you for reminding me, only now I had to learn to use brackets on my phone calculator and type the log button first.
I appreciate your explanation! I solved the problem this way: log (base 2) of 9 for an answer of 3.169925. Of course my calculator allows me to pick any base and not all calculators allow that.
@mrbobbybrown7 I initially arrived at the same value simply through trial and error, starting with pi (which I was dearly hoping it would be!), then gradually zoning in on the correct figure to 6 dp, as you gave. But after watching the video, the whole log thing made perfect sense.
I also came up with the same answer, i.e. log (base 2) 9 but my scientific calculator only has log and ln. What kind of calculator have you got that has that function? I got the answer by using a log algebra rule to get the same formula he used to get the answer, i.e. log (base b) x = log (base a) x / log (base a) b where the base a in this case is 10. I didn't know about (or more likely have forgotten) the rule where you can move the exponent in a log to be a multiplier of the log. Good to know!
Thanks! That was the best lesson I’ve had about math in my entire life it feel great to be able to finally understand how to properly figure out math in the order it should be done . I am in my 70’s and you could only imagine how it feels to be now smarter the my grandchildren😂😂😂😂
What the last lady said!!! I’m 53, retraining as an electrician and not impressed with my tutors grasp of maths so decided to revisit where i gave up at school - calculus! I found your channel and have had no sleep since! I love the way you present and the brisk but sensible pace. Thank you from the bottom of my pencil case!!
This might bear out my contention that some STEM instructors are (a) not fully immersed/versed in their subject or (b) might have a little fear of the subject.
Calculus took all the inane math they taught us in high school and put it to use, literally made me go, "AH HA! That's why they taught us this in high school!" in a Calc101 lecture one day. The prof got a laugh out of that. You know, like quadratic equations, etc.
I am 79 now and have had a professional carreer and graduated twice in college both in arts and in science. I had to take algebra three times to paas it. I am enjoying relearning algebra only now I am understanding it thanks to this exellent teaching. First time knowing how to use log functions. It's really fun!.
Applying the concept of an inverse avoids almost all the little tricks and sayings that otherwise folks would need to remember. If you have multiplication, undo it with division. If you have a power, undo it with a root. If you have an exponential, undo it with a log. And if you have a log, undo it with an exponential. I've had amazing results with students when I explain it this way. Good luck all!
A lot of people on the comments complaining about the guy "delaying" and going through "unnecessary long explanations" before solving the main problem, but i might say that i totally disagree with that, i find it pretty difficult to take my brain to focus on memorizing or learning something when it is out of context, so i just LOVE SO MUCH this guy's videos, they always give lots of contextualization and that helps me out so much, i wonder if math at school would be more fun if my teachers stopped cutting through a lot of "unnecessary advanced things for your level" and started to focus more on theoric explanations before the whole computation thing, it would make things a lot more smooth specially in physics in my opinion 😼
Most people learn from repetition. Solve it. Then go over it again with a longer explanation and what type of procedure you are using. KISS. Its a 16 min video, that can be done in 5 minutes....
Hmmm.... I took Calculus and Algebra 3/Trigonometry in high school. The handheld calculator wasn't invented or in mass production and we used a SLIDE RULE. I passed those classes in 1967 and have never used a slide rule since. However, it might be nice to see you math guys actually use one to depict the olden days on one of your videos. Thanks! 👍
I’m 45 now, and our Math Teacher way back then was every teen boy’s dream, she may have explained log quite perfectly, not sure, but its great to listen to your explanation while being able to focus!😂
I commend you for a brilliant description of the use of logarithmic math that will inform those whose first response to such problems is fear. Your description will remain with the student who has such a reaction!!!! Bless you!
As an aeronautical engineer I struggled with maths all my life and now , thanks to your explanations, at the age of 88 years the penny is beginning to drop. Many thanks for your wonderful tuition.
I didn't know until I was in my late 30's that I liked maths (sorry I'm English so we called it MATHS). I didn't know I loved maths until I found you at the grand old age of 66. I injured my brain when I had a fight with a car on a crossing a few years back and thought my intelligence had been knocked out never to wake up but it has so thank you. Give me a few maths problems, paper and pencil and I'm happy.
So sorry about your fight with the car. It's so nice to see I'm not alone with a love for maths! BTW...I didn't know the English called it maths. I always thought it was autocorrect throwing in an "s" My father told me our family heritage is cornish. 🥰
@@Ben-mk9ig The American term is more logical. Look at gymnastics, the shortened term is gym not gyms. That said, I don't think we'll change any time soon.
I hadn't heard of a shortened term for gymnastics but gyms would actually make more sense. Anyway the cheer crowd say acro which I take to be short for acrobatics. @@jazz2012
I dropped out of Engineering physics, and became a chef. I have always loved math, and this was fun. I remembered that it involved logarithms, but couldn't move past there. I watch a ton of math videos for entertainment, which apparently isn't a thing amongst my peers in the culinary industry... I am going to sub to your channel!
Great video. Learned this stuff in Alg 2 at age 16 and honestly have never had to solve for an exponent in 50 years since, even though I've been involved in highly technical areas the whole time. I HAVE however used straight Log, geometry and trigonometry functions a LOT. Electrical/audio, frequency/filters/phase, db all live deeply in these math zones.
@@CasaErwin Log 10 is most commonly used and referred to just as "Log" and was my meaning. I learned about natural log as well but never had to use it in real life.
In this particular problem, as is the case in most problems involving logarithms, the base is not important. You will get the same result no matter what base is used.
I've always held that someone who has really mastered a discipline can explain an element of it in terms that ANYONE can understand. You are proof of my postulate , and I thank you for your service............. one of the many who are underpaid and under appreciated in our society.
This video is precisely why i still cant do basic math. Too much additional information in between the actual lesson. Please just tell how to solve the problem and keep out the million if whens. You must have said how do we solve this? Im going to tell you right now. JUST TELL ME. sorry. im not alone in this. Just ask anyone who failed math.
sis: You are not wrong. Many of the math teachers I had in HS and Uni. were terrible; however the two or three good ones kept the fire alive. I believe the explanation used by the author is TERRIBLE! Having taught technical college for a number of years I determined that the direct solution to the given problem is the way to go, followed by supporting theory. Deeper analysis may be justified depending on the questions from the class/group. Getting bogged down in the minutiae of the theory will put half the class to sleep before the actual solution is proffed. BTY, I "solved" this problem by estimating the answer to lie between 3.1 and 3.3. Good enough for a first go-around.
I was always terrible at math in high school. Now that I’m taking college math, I’ve developed a sort of obsession with it. I love logs. They’re way more practical in real life than one might expect.
Take logs of both sides, re-arrange and the answer is log 9/log 2. (Use whatever base you like for the logarithms, natural or base 10, as long as you use the same top and bottom.) EDIT: I think logs are much easier if you're over 60 and weren't allowed to use pocket calculators in exams (which were fairly new), but had to use log tables instead...
That's what I did and agreed, although I was one of the first years permitted to use calculators, and did use log books briefly in junior school. Think of a log as "What number do you need to raise the log base to, to get the number you are determining the log of. In this case, Log2(9) . If your tables or calculator doesn't have the log base you are looking for (in this case 2), then divide your log by the log of the base you are looking for.
@@nickhill9445 You don't need to think about different bases for logarithms for this problem at all. All you need to know is log(x^y)=y*log(x), for logarithms of any base. So 2^x=9 gives log(2^x)=log(9) which gives x*log(2)=log(9) and dividing both sides by log(2) gives x=log(9)/log(2).
@@jerry2357 That is true, however, if you think about it as I did, then if you already have a log of the same base, the answer is immediately log(9). Take, for example, e^x=9. You could think ln(e^x)=ln(9) => x ln(e)=ln(9) factor out ln(e) => x=ln(9). Or if you understand logs from the base perspective, you jump straight to x=ln(9).
John starts giving you the solution at 5:38. We love you Mr youtube mathman.! Keep your videos coming, Some complaints here on this thread about the long intro, but you describe from the very basics which alot of students need to know, and maybe understandably fustrating to listen to by those students who already know. You are helping a lot of people out there, keep up the good work!. The "Bacon And Eggs" is a brilliant way to remember the Log set up. Very helpful indeed,
I can remember using logarithms in A level maths when in Australia. Like many, I passed my maths exams, at university entrance level, without ever twigging they are simply means of calculating square roots! I must have got the process right in complex formulaic work, but thank you for finally explaining the logic, 56 years late, but thank you. Now, back to Excel.
It's log₂ 9 by definition of log. And it can be rewrited as lg 9 / lg 2 or ln 9 / ln 2. I think the original form is more beautiful. Also I expected you to show how to get 3 decimal digits witout calc as you said in the begining of the video, but you didn't :(
Ive been learning algebra and all wonderful mathematics from you i never learnt at school, im 60yrs. I realised i never understood the formula. Thanks to you i can do algebra in my head now just looking at your tests. THIS HOWEVER HAS ME STUMPED. I CANNOT UNDERSTAND YOUR EXPLANATION OF THE FORMULA. OFF TO TAKE A VALIUM, IM GOING CRAZY 🤪.
I don't know what drew me to your blog, but it is really interesting to find how much I have forgotten since I was at school and later did my degree, I am seventy now and don't really have much use for maths, except I have a couple of grand children one two and one seven, I am helping the seven year old to learn to read, maths could be next. So I decided to subscribe to your channel and relearn or refresh or even learn new things in Math. Might help prevent the mind addling as well. I love the way you explain things so clearly, you must be a talented teacher.
When clearing out our loft many years ago, I found my trusty Thornton slide rule. I explained to my then young son that it was what we used for a calculator back in the day. He ran to my daughter shouting "Dad's got a wooden calculator!" I always liked it, and the batteries never went flat...
Fynny thing... I still have a slide rule that I used many, many years ago. I was just looking at it the other day and found that I could no longer figure out how to use it.
Yes, in fact that’s how I solved the problem in about 30 seconds. Using the log-log scales of an old K&E log-log duplex decitrig (4081-3) slide rule, I got 3.17 as the answer. One of the beauties of the old analog slide rule is that it simultaneously shows 2-to-the-x solutions for an entire range of numbers once the problem is set up (but with somewhat limited precision).
When I spotted your video I couldn't prevent myself from watching it through. I forgot about logarithms completely so thanks for that. Wish I had you as a teacher back in high school.
This one is really cool; I did this in my head knowing 2 to the power of 3 = 8 so I knew the exponential had to be 3.something. So I used 2 ex X = 1 where ex = ,13 so the remainder for 3 is .17 therefore my answer is 3.17, slightly over but close enough in my head
@@BearBryant-u8w this is why I unsubscribed from his channel. Too much rambling and his childish "Mr RUclips Math Man" really gets on my nerves. I will find someone else more mature to listen to.
Yep, his teacher would have deducted at least a point and likely more for forgetting how to round properly. You wouldn't want to do this on the space program.
@@billyhancock7851 it's simply what level of accuracy you're talking about. 3.17 could mean anything from 3.165 to 3.1749999... 3.170 however limits that to 3.1695 to 3.17049999...
@@WombatMan64 My bad! I thought that in math, 3.17 meant 3.17! Not +/- 3.17. Also it did come up with 9.000. I guess that I have a lot to learn. I should have paid more attention in school 🏫!
Yay!!it’s so much easier to use with the calculator.thank you! I just subscribed you.your channel is a big help for me.I’m 54y/o studying algebra 😅!I have headache all the time !I found your channel very timely.❤been watching you for days now.thank you very much!
When I was in school in the 60's and early 70's we had no calculators and used log tables. I remember how much I hated logs. Exponents were ok but not logs. Thanks for the info. I am another senior who is hooked.
I totally agree. I would’ve also appreciated how to solve it WITHOUT a calculator. Log 9 divided by log 2 equals 3.169? How do you manually come to that conclusion? What’s the value of log? Is it 10 or 7, and how does that apply? I ended up with more questions than answers here.
Agreed, this guy likes the sound of his own voice. Anyone struggling with mathematics will learn nothing here as they would be swamped by the information.
@@Kekahili702 a log is the power of 10 that equals a number. In the old days like when I went to school we had logarithm tables to look up. They weren't that painful really
Always take the log of the base which in this case is 2. Simple : log2(2^x) = log2(9) => X=log2(9)=> x = log2(3*3)=> x = log2(3) + log2(3)=> x= 2log2(3)
I am iin my 60's and have always enjoyed math. This can be very confusing! I wish you would let us know when we would use this in every day life. So that I can explain it to my grandchildren that struggle with math.
Everyday life just does not call for this. Addition, subtraction, division and multiplication should get you through life. Olives: 3 for $5.00. How much is one? THAT'S what ya need. Unit pricing basically. If you can't remember the last time you used exponents, THERE'S the reason - ya don't need them...IMHO. 😁
@@brucestaples4510 Thank you for your response! I have learned so much from your youtube site. I have 5 children and some thrive on math and others struggle. Many will ask what they need it for and you have answered as I have told them. There father was an accountant and loved math I believe that they found this as something that they enjoyed together. Again thank you for your quick response. Take care Vickie
@@brucestaples4510 Totally agree, better by far to get your grand kids totally conversant with mental arithmetic being able to add, subtract, multiply, divide, and average in their heads, without a calculator, will be far more beneficial to them, they need this to pass their exams they need mental arithmetic to live comfortably for the rest of their lives. Basics first!!
I didn't have an advanced calculator handy, so I used similar logic that the value of X should fall between 3 and 4. From there, I did it by inspection. My first guess was 3.333 and that was a bit over 10, so then I tried 3.2 and that was 9.18 ... after that, it didn't take too long to get it. 😄
@@CasaErwin - Like I said, I did it "by inspection." This is a valid technique in mathematics when a person does not have a calculator. There has to be a starting point, which involves an initial "guess," albeit, it would be an educated guess, based on experience, etc. By your logic, you would never approve of the Scientific Method which is to take a situation worthy of investigating and stop there, rather than creating a hypothesis,, which in essence is also an educated guess. We would have no technological advances if people didn't start processes with guesses (hunches). Jeepers.
Very simple! All you need to know is what exponential and logarithmic functions are and what their relationship to each other is. They undo each other. In other words, they're inverse functions, like addition/subtraction, multiplication/division, etc. By definition, raising a logarithmic expression to a power is the same as multiplying by the exponent the logarithmic expression without the exponent. 2^x=9 ln(2^x)=ln9 x*ln2=ln9 x=ln9/ln2 x=2.19722/0.694315 x=3.1699 2^3.1699=9 .
I wish I'd had teachers that took time to explain all this stuff like you do. Most of mine just expected us to know it by "reading the books". That's tough for visual learners. May I ask which program you are using for the illustrations? I'll be joining your Patreon crew. This stuff is gold! -Steve
"log base 2 16 is equal to 4" is a very sloppy way of saying this that confuses people who need such a basic review. It should be at least "The log base 2 of 16 is equal to 4", better "The logarithm of 16 to the base 2 is equal to 4. (And it's not "log rhythm".)
Totally agree with you. I'm a meteorologist, and I have already forgotten most of the math we needed to learn to get through it. This channel is a good place to start... without the intimidation factor.
I'm an old git but you have reminded me of the simple joy and true beauty of mathematics. Algebra in particular. Had to sub. Also you are a top drawer educator.
Either log base 10 or natural log (ln) can be used to solve this problem. Take the log (or ln) of both sides, then use the log (or ln) property to pull the the exponent to be multiplied by the log (2) or ln(2). xln(2) = ln(9). x = ln(9)/ln(2) = log(9)/log(2) = 3.17. The base of the log doesn't matter.
@@davedixon2068, Anyone who has studied math, knows x log2= log9. Those who do not have, can not understand this concept unless they take math class afresh. So the title of the vdo tends to ridicule those "some". The post could not teach math, enough to explain the concept of Log to answer your " Why" in the VDO.
@ Chuck Pierce , In fact ' log x to the base a =b' means x raised to the power of a =b. X can be any number, be 10, 2 or e. The logic of Log does not differ. By the way, your profile and interest is impressive. ❤ from Bharat ie India.
@@madhusudangupta3661 You dont get it ,I am not asking why log whatever does whatever I am asking why work out any of these math problems using techniques that you will never use ever in your life
I am 77, but still remember vividly the stuff my Math teacher tried to teach us. For this reason I will add my 10 cent from memory: The "log" term is generally used if you chose a base of your own (see like in the video from 7:04' for the base A and base 2). In case you wish to use the "logarithmus naturalis" with the base "e" (the Euler number e = 2.7182818...), you mark this not with "log", but with "ln" (see video from 9:20'). However, if you decide to use the number "10" for your base (as in the video's solution), you should apply not "log", but "lg" - this is exactly what my digital calculater tab is showing! 🙂
Math teacher here. That took me 5 seconds. I envy the time you have to give such a deep explanation. (Meanwhile I teach 7-12 graders who are lacking the most basic 2nd-5th grade skills…but hey, at least they *KINDA* can use a calculator!)
I think what our procedure 900 years ago was to isolate the x. By multiplying both sides by the base. Which turns out to be the same thing, but I think that's how they put it to us back when I was much younger.
I haven't used logarithms in maths for more than 50 years but when the problem surfaced I looked for the simplification that removed the powers and very quickly decided that using logs was the quickest way. I then waded through 10minutes of confusing explanation to verify that what I thought was correct. I am just glad our maths teachers didn't teach us in this manner.
Whoa! Now you're talking Advance Cave Man from the 1950's to at least the 1980's who had access to the magic stick called A Slide Rule. I'm a cave man from the 1960's with just a pencil with an eraser and stacks and stacks of paper.
for 2^x = 9, the solution is x = log2(9). When you substitute you get 2^log2(9), the 2 and the log2 cancel out and you are left with 9 as a regular number, then it's just 9 = 9.
WHO the heck, over 60, comes on RUclips and watches math videos just for fun? Oh, that's right, *I* do! 😁 Fun, AND to learn something I didn't know before. 😉
Thanks for the explanation. I have a 3 year old daughter who already counts to 1000, she got to 200 and said, should I do all of them? She's amazing and smart, so I'm learning up ahead of time because I know I'm going to need to keep up (I am 54). As an outside observer right, If a number is squared, it means its a 2 dimensional square flat object(x=y). Cubed suggested its a 3d object,(x=y=z) and then things get interesting because it goes beyond the realm of physical logic and we enter the world of theoretical mathematics. Is that what it is? In reality the 4th dimension is time as we have labelled the situation in physics, but in mathematics the fourth one is treated same the as the third when we talk exponentially. Food for thought.
Take log of rack side . Use rule that number raised to power is the same as multiplying power by log of that number . So we have xlog2 = log 9 . Then x = log9/log2 . This gives x = 3.1698 . So 2^3.1698 = 9
log a (b) / log a (c) = log c (b) | Where a and c is the base number. In this case, we can choose any base. Let's use base 10: log(9) / log(2) = log 2 (9) | Where we use the base number 2 Now, since 9 = 3^2, we can express log 2 (9) as: log 2 (9) = log 2 (3^2) = 2 log 2 (3) I suppose this is a somewhat better answer than it's ≈ 3.170
Simple Algebra teaches you to isolate the variable(s) in question and you need, at a minimum, the same number of equations equivalent to the number of unknowns (variables). In the above case, its one, X; therefore, in order to solve for the variable X, a single equation will suffice. In order to isolate the variable, Alegbra teaches us to perform the opposite operation for what is presented. The opposite operation of exponential growth is logarithmic growth or they are inverse from one another. Given the following equation: 2^X = 9; To solve for the exponent (X), need to perform the opposite operation for what we see and take the logarithm or log of BOTH sides of the equation: log (2^X) = log (9) In order to change this equation into another form we can better work with we will substitute one equal value for another. Apply the Power Rule of Logarithmn that states: log (M^N) is equal to N log M where: log (2^X) = log (9) is equivalent to the following: X log (2) = log (9) Since X is multiplied by one term, we will isolate X by performing the opposite operation as what we see. Isolate the variable X by divididing BOTH sides of equation by log(2): X log (2) / log (2) = log (9) / log (2) is equivalent to the following: X = log (9) / log (2) By use of a calculator: X = 3.16992500144 Plug back into original equation to verify that: 2 ^ (3.16992500144) = 9 Although, it may appear complicated at first, but knowing that log is the inverse of exponent and the power/exponent rules it was quickly solved in under 2 mins. The challenge of math comes from forgetting the lower levels of mathematices that come BEFORE the one you are working with. It really does just boil down to the basics...
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As a teenager, if i I could have looked in the future and discover I'd be studying algebra/math as a senior (60 year old) for FUN I'd think I'd lost my mind😂❤❤❤
Same here, I let myself fall victim to the girls can't do the math myth of my day. I have since then discovered I just love doing problems to relax
Me too at 45 😂
I feel the same and I'm 62.
I always like algebra, plus geometry, trigonometry. It was plain simple stuff in the early years I hated.
For sure!!!!!!!
It’s SO reassuring to recall/relearn it through this very patient teachers guidance!
It’s bothered me that I’ve not used it and therefore have lost it, so yes! It IS. both fun and cognitively reassuring to do it once again here!
The video starts at 11:15 for those wondering
Yes, I agree. He took too long to get to the point.
If I were in your class I would have fallen asleep half way through your explanation.😂
Thank you
Thx bro
To solve this what needed is the definition of the logarithm, a calculator and 15 seconds. 🇦🇺
Just reading some of the comments. I find it interesting how many seniors (like myself) enjoy doing this for fun. Great Mental Exercises. Thanks!
I'm 58. Stumbled across this video. I love reading the comments
Can a 39ish apply for the club?
@@Fernando-qd4ur Such a child!! In 21 days, I will be 89 years old.
@@CasaErwin 🤣🤣🤣
I m 53 now, enjoying watching this
I enjoy your classes. In 1959 I was in hospital for 6 weeks and home for 6 weeks, back in junior math without ever opening a book, I was the only one in the class that could solve homework.Then in 2013 I had chemo and radiation and had to start using a calculator for other than trig functions. Watching your classes some of it comes back. Thank you
Thank you for offering this here!!!
I am part of the 60+ club here!
✨🎉😅
It’s SO reassuring to recall/relearn it through this very patient teachers guidance!
It’s bothered me that I’ve not used it and therefore have lost it, so yes! It IS. both fun and cognitively reassuring to do it once again here!
You are indeed doing a great service to many, kind sir!
Again, thank you!
🥰 totally agree
I’m 77, going on 78 tomorrow and I’m here, too.
Thank you for this math lesson, that brought back many memories!
RL
LOL - 60 is just right around the corner for me. (Where did the time go??) I was not crazy about math in high school as it seemed like they always went too fast. I liked my math teachers, though, I just had trouble keeping up. In college, I began to like it a bit more as made more sense the second time around - and I only had math classes every other day. Now it has become an enjoyable of a hobby for me next to collecting classical music CD's. BTW, one of my former math teachers, dear old Mr. Robert Parks passed away one year ago this month (in January 2023) at the age of 93 - may he rest in eternal peace!!
As an engineering student it was seldom the calculus that gave me problems, it was the algebra that gave me fits because it was so far back in my education that I was out of practice. Practice and repetition keep the skills fresh.
True. When I started my engineering education I signed up for Trigonometry and found out I forgot Algebra from high school even though I got A's. So I dropped out and took College Algebra. Long story short I finished all the math requirements with A's and graduated with B. S. in Mechanical Engineering PI TAU SIGMA the International Honor Society for Mechanical Engineers.
As an engineer, I worked it out *numerically* by trial and error starting at 2^Pi (just for fun), and adding decimal digits and got 2^3.1699250014425 = 9.
What is the old saying?...
"If you want to learn algebra, take calculus."
My wife does word puzzles to try to stay sharp. She is 70. I am 72 and trying to stay sharp doing and re-learning math. My 11 yr old granddaughter helped me get started by asking me to help her with her 6th grade math. 😅
🥰❤
I am of a similar age and I have on occasions tried to help the younger generation (including my daughters) with their maths problems and mostly gave up because the current method of teaching is so vague as to be incomprehensible and to me defies logic. One attempt was to solve a problem for a colleagues daughter, where I built up the answer from the information given. The working out was to me at a higher level than I thought was appropriate for his daughter's age. A couple of days later I was informed that the pupils were not to work the answer out but to guess it! Whilst its obvious that through life you estimate what answers might be so that you can validate the actual solution but to just simply guess the answer to a question does not bode well for the human race. Imagine if NASA guessed all the manoeuvre inputs for a trip to the Moon!
there is no scientific evidence to prove word puzzles prevent dementia, and other issues. More so there is evidence that healthy eating, and exercise prevents all age related issues.
JOY and DANCING FEET! I rose to the challenge and recalled the solution method from high school math before I had to resort to watching the video. I'm 64, so it has been a while since I needed to do this kind of math. A small thing, but it made my day. A similar event happened when my high school son came up to me and asked how to solve a calculus problem 20 years ago.
omg me too..clicked on the vid to check my maths, lol, 66 yrs old, figured it out in 3 .1 seconds, excellent speed test for us, huh?
Must of done this 30-40 years ago and completely forgotten because I've never needed to use it. Quite satisfying that it came back when explained, I'll be watching more.
I would use logarithms for this:
2^x = 9
log of both sides log(2^x) = log(9)
x log(2) = log(9)
x = log(9)/log(2)
Of course you need log tables to get the solution. Maybe there's another way. But since 2^3 = 8 and 2^4 = 16, we know the answer will be somewhere between 3 and e4.
Calculators
Yes, I would use logarithms but with the help of calculator. Never got to learn how to use the log tables in school. Am born in the early 70s
WHile you're at it might want to bust out ye ole Abacas...
There isn't a solution to this problem, because there isn't a definite solution for it
Maybe this or that yada, yada.blah
Its 55 years since I first learned this material and now I have almost completely forgotten it. We had Log Books back then, calculations were slower and calculators were only just emerging. I never used manual algebra or calculus in my working life as computer programs took care of multiple data streams and operations almost instantly. Now, I'm relearning the fundamentals solely to keep my mind active. Thanks for your explanations and patience.
78 calculators didn't exist in my school 14:46 years. We used llog books.
Dad, an engineer, bought himself a Texas Instruments model and in 1974 he bought me a Colex. It was the first calculator in my year group but we still had to know how to use log books and slide rules well before and well after 1974! @@mariondavis5735
@@mariondavis5735 Most of the students I interact with would have a meltdown if handed a log book.
Same here It has be 45 years for myself I bet you used a. Slide rule
@@johnplong3644 I actually still own two. One is my grandfather's that he used during flight training in the Marines back in WWII.
Great!! I went through Calculus III and Differential Equations many years ago and nobody explained to me like this
what a log is. Thanks. I'm thinking of studying Math again to learn all that I forgot.
I actually enjoyed this lesson.I'm retired and just when I thought that I no longer had use for this stuff, I just found out how wrong I was.I think I just found something that I cam actually gravitate to.Keep the wheels in the old brain turning. Thank you so much. Keep up the good work.
I think it's the story about wisdom. When we're old we can actually see the usefulness of things we deemed as useless as kids. I ruminate over this thought every time I use algebra.
It also might be a good idea if teachers would employ mathematics to real life situations.
Thank you for explaining it so clear. In the Netherlands I learned about exponential equations and logarithms at school long ago. Thank you for reminding me, only now I had to learn to use brackets on my phone calculator and type the log button first.
I appreciate your explanation! I solved the problem this way: log (base 2) of 9 for an answer of 3.169925. Of course my calculator allows me to pick any base and not all calculators allow that.
That's what I did, didn't he round it incorrectly to 3.169? To three decimal places should be 3.170. Maybe this is already in the comments.
@@JohnMasseria yep, exactly why I didn't watch it. He lost me there. Shouldn't make a video about math (AND ROUNDING OFF) when you can't.
@mrbobbybrown7 I initially arrived at the same value simply through trial and error, starting with pi (which I was dearly hoping it would be!), then gradually zoning in on the correct figure to 6 dp, as you gave. But after watching the video, the whole log thing made perfect sense.
@@JohnMasseria- technically, there are different methods of rounding. “Round to the floor!” 😅
I also came up with the same answer, i.e. log (base 2) 9 but my scientific calculator only has log and ln. What kind of calculator have you got that has that function? I got the answer by using a log algebra rule to get the same formula he used to get the answer, i.e. log (base b) x = log (base a) x / log (base a) b where the base a in this case is 10. I didn't know about (or more likely have forgotten) the rule where you can move the exponent in a log to be a multiplier of the log. Good to know!
Thanks! That was the best lesson I’ve had about math in my entire life it feel great to be able to finally understand how to properly figure out math in the order it should be done . I am in my 70’s and you could only imagine how it feels to be now smarter the my grandchildren😂😂😂😂
What the last lady said!!! I’m 53, retraining as an electrician and not impressed with my tutors grasp of maths so decided to revisit where i gave up at school - calculus! I found your channel and have had no sleep since! I love the way you present and the brisk but sensible pace. Thank you from the bottom of my pencil case!!
This might bear out my contention that some STEM instructors are (a) not fully immersed/versed in their subject or (b) might have a little fear of the subject.
Maybe if he shortened his lecture then you could get some sleep duh!
Calculus took all the inane math they taught us in high school and put it to use, literally made me go, "AH HA! That's why they taught us this in high school!" in a Calc101 lecture one day. The prof got a laugh out of that. You know, like quadratic equations, etc.
I am 79 now and have had a professional carreer and graduated twice in college both in arts and in science. I had to take algebra three times to paas it. I am enjoying relearning algebra only now I am understanding it thanks to this exellent teaching. First time knowing how to use log functions. It's really fun!.
What? 3x, wd two courses, your teacher is terrible.
Applying the concept of an inverse avoids almost all the little tricks and sayings that otherwise folks would need to remember. If you have multiplication, undo it with division. If you have a power, undo it with a root. If you have an exponential, undo it with a log. And if you have a log, undo it with an exponential. I've had amazing results with students when I explain it this way. Good luck all!
And if you have addition, undo it with subtraction and vice versa. :)
@@Kleermaker1000m
A lot of people on the comments complaining about the guy "delaying" and going through "unnecessary long explanations" before solving the main problem, but i might say that i totally disagree with that, i find it pretty difficult to take my brain to focus on memorizing or learning something when it is out of context, so i just LOVE SO MUCH this guy's videos, they always give lots of contextualization and that helps me out so much, i wonder if math at school would be more fun if my teachers stopped cutting through a lot of "unnecessary advanced things for your level" and started to focus more on theoric explanations before the whole computation thing, it would make things a lot more smooth specially in physics in my opinion 😼
Cant wait 🚶long que-we..🥴
Most people learn from repetition. Solve it. Then go over it again with a longer explanation and what type of procedure you are using. KISS. Its a 16 min video, that can be done in 5 minutes....
Hmmm.... I took Calculus and Algebra 3/Trigonometry in high school. The handheld calculator wasn't invented or in mass production and we used a SLIDE RULE. I passed those classes in 1967 and have never used a slide rule since. However, it might be nice to see you math guys actually use one to depict the olden days on one of your videos. Thanks! 👍
I’m a 78 yr. Old woman and only had 1 yr. of collage, but had Algebra 1 & 2 in H.S., but I really love math. This is familiar, I like it. 😊
if only they had such good videos when i was in 8th grade learning pre algebra! Math is one subject where videos really make a difference!!
It's approximately 3.169925, so rounded to 3 decimal places would be 3.170
Yes, he rounded it wrong. He just skipped decimals, no rounding what so ever.
@@johnnyrosenberg9522 nobody cares dude
@@theowenssailingdiary5239That doesn't bother me at all, but thanks for caring.
True.
16 9 9 25 all can be rooted squarely is this a coincidence ?
Use log-base 2 and it's even quicker. x = log2(9). Plug log2(9) into the calculator and you get 3.1699 directly.
My calculator keeps putting the parenthesis around the 2
@@GenXFarmer77 In this case it doesn't make any difference which base you use. Any base will give you the same answer.
@CasaErwin tell that to my calculator lol
In Excel, you can use either =log(9,2) or =ln(9)/ln(2) or =log(9)/log(2), or if you really want =2*log(3,2) or something like that.
I am a math lover and this class stands perfect to me! Thanks!
I’m 45 now, and our Math Teacher way back then was every teen boy’s dream, she may have explained log quite perfectly, not sure, but its great to listen to your explanation while being able to focus!😂
I commend you for a brilliant description of the use of logarithmic math that will inform those whose first response to such problems is fear. Your description will remain with the student who has such a reaction!!!! Bless you!
As an aeronautical engineer I struggled with maths all my life and now , thanks to your explanations, at the age of 88 years the penny is beginning to drop. Many thanks for your wonderful tuition.
lol, hahaha
Better late than never.
I love your site! Great explanations. I’m 72 and your channel brings back a lot of memories of high school math. Still remember this stuff.
I didn't know until I was in my late 30's that I liked maths (sorry I'm English so we called it MATHS). I didn't know I loved maths until I found you at the grand old age of 66. I injured my brain when I had a fight with a car on a crossing a few years back and thought my intelligence had been knocked out never to wake up but it has so thank you. Give me a few maths problems, paper and pencil and I'm happy.
So sorry about your fight with the car. It's so nice to see I'm not alone with a love for maths! BTW...I didn't know the English called it maths. I always thought it was autocorrect throwing in an "s" My father told me our family heritage is cornish. 🥰
I thought it odd that the English call it maths until I realized that no one says they are doing mathematic.
@@Ben-mk9ig The American term is more logical. Look at gymnastics, the shortened term is gym not gyms. That said, I don't think we'll change any time soon.
I hadn't heard of a shortened term for gymnastics but gyms would actually make more sense. Anyway the cheer crowd say acro which I take to be short for acrobatics. @@jazz2012
I dropped out of Engineering physics, and became a chef. I have always loved math, and this was fun. I remembered that it involved logarithms, but couldn't move past there. I watch a ton of math videos for entertainment, which apparently isn't a thing amongst my peers in the culinary industry... I am going to sub to your channel!
Great video. Learned this stuff in Alg 2 at age 16 and honestly have never had to solve for an exponent in 50 years since, even though I've been involved in highly technical areas the whole time. I HAVE however used straight Log, geometry and trigonometry functions a LOT. Electrical/audio, frequency/filters/phase, db all live deeply in these math zones.
Same here 🤝
straight Log???? Not familiar with that term. Is it anything like natural Log?
@@CasaErwin Log 10 is most commonly used and referred to just as "Log" and was my meaning. I learned about natural log as well but never had to use it in real life.
In this particular problem, as is the case in most problems involving logarithms, the base is not important. You will get the same result no matter what base is used.
I've always held that someone who has really mastered a discipline can explain an element of it in terms that ANYONE can understand. You are proof of my postulate , and I thank you for your service............. one of the many who are underpaid and under appreciated in our society.
This video is precisely why i still cant do basic math. Too much additional information in between the actual lesson. Please just tell how to solve the problem and keep out the million if whens. You must have said how do we solve this? Im going to tell you right now. JUST TELL ME. sorry. im not alone in this. Just ask anyone who failed math.
Don't watch the video go somewhere else
He talks to much
sis: You are not wrong. Many of the math teachers I had in HS and Uni. were terrible; however the two or three good ones kept the fire alive.
I believe the explanation used by the author is TERRIBLE!
Having taught technical college for a number of years I determined that the direct solution to the given problem is the way to go, followed by supporting theory.
Deeper analysis may be justified depending on the questions from the class/group.
Getting bogged down in the minutiae of the theory will put half the class to sleep before the actual solution is proffed.
BTY, I "solved" this problem by estimating the answer to lie between 3.1 and 3.3. Good enough for a first go-around.
It's almost like they get caught up in bragging about how good they are at math.. it's weird, I can't believe it still happens. 🤷
I was always terrible at math in high school. Now that I’m taking college math, I’ve developed a sort of obsession with it. I love logs. They’re way more practical in real life than one might expect.
Take logs of both sides, re-arrange and the answer is log 9/log 2. (Use whatever base you like for the logarithms, natural or base 10, as long as you use the same top and bottom.)
EDIT: I think logs are much easier if you're over 60 and weren't allowed to use pocket calculators in exams (which were fairly new), but had to use log tables instead...
That's what I did and agreed, although I was one of the first years permitted to use calculators, and did use log books briefly in junior school.
Think of a log as "What number do you need to raise the log base to, to get the number you are determining the log of. In this case, Log2(9) . If your tables or calculator doesn't have the log base you are looking for (in this case 2), then divide your log by the log of the base you are looking for.
@@nickhill9445
You don't need to think about different bases for logarithms for this problem at all.
All you need to know is log(x^y)=y*log(x), for logarithms of any base.
So 2^x=9 gives log(2^x)=log(9) which gives x*log(2)=log(9) and dividing both sides by log(2) gives x=log(9)/log(2).
@@jerry2357 That is true, however, if you think about it as I did, then if you already have a log of the same base, the answer is immediately log(9).
Take, for example, e^x=9. You could think ln(e^x)=ln(9) => x ln(e)=ln(9) factor out ln(e) => x=ln(9). Or if you understand logs from the base perspective, you jump straight to x=ln(9).
Just what i thought , it takes 1 minute to explain. Not 15 mins 🥱
@@nickhill9445 the question is not e^x=9 but 2^x=9 so x=ln(9)/ln(2) and not x=ln(9) as you stated.
John starts giving you the solution at 5:38.
We love you Mr youtube mathman.! Keep your videos coming, Some complaints here on this thread about the long intro, but you describe from the very basics which alot of students need to know, and maybe understandably fustrating to listen to by those students who already know. You are helping a lot of people out there, keep up the good work!. The "Bacon And Eggs" is a brilliant way to remember the Log set up. Very helpful indeed,
Thank you for your calm demeanor and clear explainations. Do you have videos on statistics?
I can remember using logarithms in A level maths when in Australia. Like many, I passed my maths exams, at university entrance level, without ever twigging they are simply means of calculating square roots! I must have got the process right in complex formulaic work, but thank you for finally explaining the logic, 56 years late, but thank you. Now, back to Excel.
It's log₂ 9 by definition of log. And it can be rewrited as lg 9 / lg 2 or ln 9 / ln 2. I think the original form is more beautiful.
Also I expected you to show how to get 3 decimal digits witout calc as you said in the begining of the video, but you didn't :(
Ive been learning algebra and all wonderful mathematics from you i never learnt at school, im 60yrs. I realised i never understood the formula. Thanks to you i can do algebra in my head now just looking at your tests. THIS HOWEVER HAS ME STUMPED. I CANNOT UNDERSTAND YOUR EXPLANATION OF THE FORMULA. OFF TO TAKE A VALIUM, IM GOING CRAZY 🤪.
This should be a 3 minute video.
I don't know what drew me to your blog, but it is really interesting to find how much I have forgotten since I was at school and later did my degree, I am seventy now and don't really have much use for maths, except I have a couple of grand children one two and one seven, I am helping the seven year old to learn to read, maths could be next. So I decided to subscribe to your channel and relearn or refresh or even learn new things in Math. Might help prevent the mind addling as well.
I love the way you explain things so clearly, you must be a talented teacher.
All of a sudden I have a desire to learn the math I ignored 26 years ago. Just wanted to say thanks for posting.
Sincerely,
Your 42 year old student 🙂
Well. Solution is very simple.
2 power x = 9
X log 2 = log 9
X = log 9 ÷ log 2
X = 0..9542 ÷ 0.3010
X = 3.17 is the answer
We always used our slide rules, pre small calculator days, to solve these types of problems . the slide rules were fun to use .
Isaac Asimov's stories had a lot of references to them, and it's funny how they disappeared so quickly despite being in his visions of the future.
Slide rules and log tables.
Brought back memories
When clearing out our loft many years ago, I found my trusty Thornton slide rule. I explained to my then young son that it was what we used for a calculator back in the day. He ran to my daughter shouting "Dad's got a wooden calculator!"
I always liked it, and the batteries never went flat...
Fynny thing... I still have a slide rule that I used many, many years ago. I was just looking at it the other day and found that I could no longer figure out how to use it.
Yes, in fact that’s how I solved the problem in about 30 seconds. Using the log-log scales of an old K&E log-log duplex decitrig (4081-3) slide rule, I got 3.17 as the answer. One of the beauties of the old analog slide rule is that it simultaneously shows 2-to-the-x solutions for an entire range of numbers once the problem is set up (but with somewhat limited precision).
When I spotted your video I couldn't prevent myself from watching it through. I forgot about logarithms completely so thanks for that. Wish I had you as a teacher back in high school.
This one is really cool; I did this in my head knowing 2 to the power of 3 = 8 so I knew the exponential had to be 3.something. So I used 2 ex X = 1 where ex = ,13 so the remainder for 3 is .17 therefore my answer is 3.17, slightly over but close enough in my head
No, yours is exact! To 3 decimal places, it is 3.170 but to 4 decimal places, it is 3.1699.
x = ln9/ln2.
How can doing anything to a 2 with a 3 make 8??
Thanks for the clarity. I was struggling with this one. Can't believe something looking so simple can be so intense.
Am so grateful to be reviewing all this fun math and you are a fabulous teacher.
Thank yoy
Your a really good teacher. No explanation could be simpler and understandable. That's what I need. Simple and understandable.
I used to use a booklet for the logs (bit like aslide rule), sines and other functions. Calculators are just a handy thing to have
I should thank the channel for providing solutions/ explanations for the maths problems I dared not to ask the teachers 50 years ago!👌👌👌👏👏👏🙏🙏🙏
It's usually best to get to the point.
this guy never gets to the point
Depends on the foundational knowledge of the viewer. If this feels drawn out then it's not for you. Fast forward
He really pisses me off with all his stupid rambling
16 minutes to explain this problem is ridiculous
@@BearBryant-u8w this is why I unsubscribed from his channel. Too much rambling and his childish "Mr RUclips Math Man" really gets on my nerves. I will find someone else more mature to listen to.
Getting fascinating, right up to the point where it was noted that a calculator was needed to obtain the answer.
No calculators when I was growing up. I had a slide rule and we calculated Logs manually as I recall.
We had a green and white book of all log values.
A slide rule is a log table
We used log tables in the early 1980s. The answer is simple. Logarithm solution.
Log9/Log2=x
As the next number is also a 9 (3.169925) you should have rounded it to 3.170. But otherwise fine.
Yep, his teacher would have deducted at least a point and likely more for forgetting how to round properly. You wouldn't want to do this on the space program.
I pressed 2& the Sq root button, then typed in 3.17 and came up with 9.000467877. Why do I need to type in the 0 on 3.17 (0)??
@@billyhancock7851 it's simply what level of accuracy you're talking about.
3.17 could mean anything from 3.165 to 3.1749999...
3.170 however limits that to 3.1695 to 3.17049999...
@@WombatMan64 My bad! I thought that in math, 3.17 meant 3.17! Not +/- 3.17. Also it did come up with 9.000. I guess that I have a lot to learn. I should have paid more attention in school 🏫!
Bad rounding cost you a mark there.
2^3.169 = 8.994 = 9 - 0.006
2^3.17 = 9.0005 = 9 + 0.0005
Therefore 2^3.17 is closest to 9.
Congratulations teacher you have genuine students🎉🎉🎉
Yay!!it’s so much easier to use with the calculator.thank you! I just subscribed you.your channel is a big help for me.I’m 54y/o studying algebra 😅!I have headache all the time !I found your channel very timely.❤been watching you for days now.thank you very much!
When I was in school in the 60's and early 70's we had no calculators and used log tables. I remember how much I hated logs. Exponents were ok but not logs. Thanks for the info. I am another senior who is hooked.
Holy crap dude, spit it out, get on with it !!! Almost 5 minutes in and you've done everything but explain how to solve the problem.
I totally agree. I would’ve also appreciated how to solve it WITHOUT a calculator. Log 9 divided by log 2 equals 3.169? How do you manually come to that conclusion? What’s the value of log? Is it 10 or 7, and how does that apply? I ended up with more questions than answers here.
Yeah I had to turn him off. I feel for the kids in his class. Did you see the video he did about pemdas? Terrible
😂😂😂
Agreed, this guy likes the sound of his own voice. Anyone struggling with mathematics will learn nothing here as they would be swamped by the information.
@@Kekahili702 a log is the power of 10 that equals a number. In the old days like when I went to school we had logarithm tables to look up. They weren't that painful really
Always take the log of the base which in this case is 2. Simple :
log2(2^x) = log2(9) =>
X=log2(9)=> x = log2(3*3)=> x = log2(3) + log2(3)=> x= 2log2(3)
I am iin my 60's and have always enjoyed math. This can be very confusing! I wish you would let us know when we would use this in every day life. So that I can explain it to my grandchildren that struggle with math.
Everyday life just does not call for this. Addition, subtraction, division and multiplication should get you through life. Olives: 3 for $5.00. How much is one? THAT'S what ya need. Unit pricing basically. If you can't remember the last time you used exponents, THERE'S the reason - ya don't need them...IMHO. 😁
@@brucestaples4510 Thank you for your response! I have learned so much from your youtube site. I have 5 children and some thrive on math and others struggle. Many will ask what they need it for and you have answered as I have told them. There father was an accountant and loved math I believe that they found this as something that they enjoyed together. Again thank you for your quick response. Take care Vickie
@@brucestaples4510 Totally agree, better by far to get your grand kids totally conversant with mental arithmetic being able to add, subtract, multiply, divide, and average in their heads, without a calculator, will be far more beneficial to them, they need this to pass their exams they need mental arithmetic to live comfortably for the rest of their lives. Basics first!!
you might use it for calculating compound interest on a loan.
@@sammic974 thats what financial advisers are for
Last math class I took was AP Calculus AB 16 years ago. Somehow, I could still figure out the answer. You took a long time explaining it.
I didn't have an advanced calculator handy, so I used similar logic that the value of X should fall between 3 and 4. From there, I did it by inspection. My first guess was 3.333 and that was a bit over 10, so then I tried 3.2 and that was 9.18 ... after that, it didn't take too long to get it. 😄
3:38 3:38 4:28 oo😊oo😊 ?;-. add e❤
In my opinion, guessing has no place in mathematics.
@@CasaErwin - Like I said, I did it "by inspection." This is a valid technique in mathematics when a person does not have a calculator. There has to be a starting point, which involves an initial "guess," albeit, it would be an educated guess, based on experience, etc. By your logic, you would never approve of the Scientific Method which is to take a situation worthy of investigating and stop there, rather than creating a hypothesis,, which in essence is also an educated guess. We would have no technological advances if people didn't start processes with guesses (hunches). Jeepers.
Very simple! All you need to know is what exponential and logarithmic functions are and what their relationship to each other is. They undo each other. In other words, they're inverse functions, like addition/subtraction, multiplication/division, etc.
By definition, raising a logarithmic expression to a power is the same as multiplying by the exponent the logarithmic expression without the exponent.
2^x=9
ln(2^x)=ln9
x*ln2=ln9
x=ln9/ln2
x=2.19722/0.694315
x=3.1699
2^3.1699=9
.
I wish I'd had teachers that took time to explain all this stuff like you do. Most of mine just expected us to know it by "reading the books". That's tough for visual learners. May I ask which program you are using for the illustrations? I'll be joining your Patreon crew. This stuff is gold! -Steve
Looks like MS Paint on a surface laptop.
5:30
I love your program. First time I ever was able to understand math.
Of course, if you prefer or are more accustomed to using log to base e, you can also get the same result from ln(9) / ln(2)
"log base 2 16 is equal to 4" is a very sloppy way of saying this that confuses people who need such a basic review. It should be at least "The log base 2 of 16 is equal to 4", better "The logarithm of 16 to the base 2 is equal to 4.
(And it's not "log rhythm".)
You will get the same result regardless of the base.
Thanks for a fun review of something I did decades ago...always good to keep the mind sharp.
I never got THIS advanced in math. It's like aerobics for the brain.
Totally agree with you. I'm a meteorologist, and I have already forgotten most of the math we needed to learn to get through it. This channel is a good place to start... without the intimidation factor.
This is easy lmao I learned in elementary
Or BRAINLESS
I'm an old git but you have reminded me of the simple joy and true beauty of mathematics. Algebra in particular. Had to sub.
Also you are a top drawer educator.
Either log base 10 or natural log (ln) can be used to solve this problem. Take the log (or ln) of both sides, then use the log (or ln) property to pull the the exponent to be multiplied by the log (2) or ln(2). xln(2) = ln(9). x = ln(9)/ln(2) = log(9)/log(2) = 3.17. The base of the log doesn't matter.
my only question here is not how but why?
@@davedixon2068, Anyone who has studied math, knows x log2= log9. Those who do not have, can not understand this concept unless they take math class afresh. So the title of the vdo tends to ridicule those "some". The post could not teach math, enough to explain the concept of Log to answer your " Why" in the VDO.
@ Chuck Pierce , In fact ' log x to the base a =b' means x raised to the power of a =b. X can be any number, be 10, 2 or e. The logic of Log does not differ. By the way, your profile and interest is impressive. ❤ from Bharat ie India.
@@madhusudangupta3661 You dont get it ,I am not asking why log whatever does whatever I am asking why work out any of these math problems using techniques that you will never use ever in your life
Thats why bother wasting your time
I am 77, but still remember vividly the stuff my Math teacher tried to teach us. For this reason I will add my 10 cent from memory: The "log" term is generally used if you chose a base of your own (see like in the video from 7:04' for the base A and base 2). In case you wish to use the "logarithmus naturalis" with the base "e" (the Euler number e = 2.7182818...), you mark this not with "log", but with "ln" (see video from 9:20'). However, if you decide to use the number "10" for your base (as in the video's solution), you should apply not "log", but "lg" - this is exactly what my digital calculater tab is showing! 🙂
This video should be titled, "How to turn a 16 second solution into a 16 minute video.*
Yes, tedious waffle.
First thing that popped into my head wasn’t I’m excited to learn the answer but Kodachrome by Paul Simon.
Instantly visible solution.
Exactly what I thought. Well, to be honest I didn't need 16 sec. 😊
😅
@9:26 … “I can’t turn this into a full, complete lecture” you did your level best… ;)
This is like watching paint dry
...and listening. Ben Stein level of monotony.
Math teacher here. That took me 5 seconds. I envy the time you have to give such a deep explanation. (Meanwhile I teach 7-12 graders who are lacking the most basic 2nd-5th grade skills…but hey, at least they *KINDA* can use a calculator!)
Why you did not show result then ? , Dorota
I think what our procedure 900 years ago was to isolate the x. By multiplying both sides by the base. Which turns out to be the same thing, but I think that's how they put it to us back when I was much younger.
I haven't used logarithms in maths for more than 50 years but when the problem surfaced I looked for the simplification that removed the powers and very quickly decided that using logs was the quickest way. I then waded through 10minutes of confusing explanation to verify that what I thought was correct. I am just glad our maths teachers didn't teach us in this manner.
You don't need 16 min to introduce log or natural log. Respecting time is crucial for a mathmatician.
Finally, somebody said something correct. I wish he had not spent all that time explaining the actual problem. Edited message. I forgot """not"".
His loves to hear himself talk and tell you how smart he is; which is the exact reason so many students are turned off by math!😮
@stanleybaehman7214
Or I don't know if youtube pays them by the time .
It's the algorithm. They need about 12 minutes.@@ube-23s
@@ube-23svideos have to be 10 minutes to get advertising revenue.
It took 16 minutes to explain what can be done instantly. The perfect length for this video is 16 seconds🌟
Now you need to show us how to complete this on a slide rule.
Whoa! Now you're talking Advance Cave Man from the 1950's to at least the 1980's who had access to the magic stick called A Slide Rule.
I'm a cave man from the 1960's with just a pencil with an eraser and stacks and stacks of paper.
Spent 34 years since I graduated. And I was love maps I try to watch in your youtube chann
if you don't have a calculator, just use your slide rule. :)
Abacus?
for 2^x = 9, the solution is x = log2(9).
When you substitute you get 2^log2(9), the 2 and the log2 cancel out and you are left with 9 as a regular number, then it's just 9 = 9.
This seems quite familiar, but when I was in school we didn't have calculators. We had to look up the logs in charts.
WHO the heck, over 60, comes on RUclips and watches math videos just for fun?
Oh, that's right, *I* do! 😁
Fun, AND to learn something I didn't know before. 😉
Thanks for the explanation. I have a 3 year old daughter who already counts to 1000, she got to 200 and said, should I do all of them? She's amazing and smart, so I'm learning up ahead of time because I know I'm going to need to keep up (I am 54). As an outside observer right, If a number is squared, it means its a 2 dimensional square flat object(x=y). Cubed suggested its a 3d object,(x=y=z) and then things get interesting because it goes beyond the realm of physical logic and we enter the world of theoretical mathematics. Is that what it is? In reality the 4th dimension is time as we have labelled the situation in physics, but in mathematics the fourth one is treated same the as the third when we talk exponentially. Food for thought.
All senior citizens who hated math is here. 😂😂
Take log of rack side . Use rule that number raised to power is the same as multiplying power by log of that number . So we have xlog2 = log 9 . Then x = log9/log2 . This gives x = 3.1698 . So 2^3.1698 = 9
You need to half the video lengthy, cos it goes on way too long.. It gets boring!
This is bringing back fond memories for me. If I am helping someone, I always tell them that algebra is a lot of remembering.
TOO MUCH UNNESSESSARY EXPLANATIONS FOR SIMPLE QUESTIONS ...
I agree..
Agreed, cut to the chase.
log a (b) / log a (c) = log c (b) | Where a and c is the base number.
In this case, we can choose any base. Let's use base 10:
log(9) / log(2) = log 2 (9) | Where we use the base number 2
Now, since 9 = 3^2, we can express log 2 (9) as:
log 2 (9) = log 2 (3^2) = 2 log 2 (3)
I suppose this is a somewhat better answer than it's ≈ 3.170
Way too many filler comments and long explanations. I zoned out many times with the monotone delivery.
Simple Algebra teaches you to isolate the variable(s) in question and you need, at a minimum, the same number of equations equivalent to the number of unknowns (variables). In the above case, its one, X; therefore, in order to solve for the variable X, a single equation will suffice.
In order to isolate the variable, Alegbra teaches us to perform the opposite operation for what is presented.
The opposite operation of exponential growth is logarithmic growth or they are inverse from one another.
Given the following equation: 2^X = 9;
To solve for the exponent (X), need to perform the opposite operation for what we see and take the logarithm or log of BOTH sides of the equation:
log (2^X) = log (9)
In order to change this equation into another form we can better work with we will substitute one equal value for another.
Apply the Power Rule of Logarithmn that states: log (M^N) is equal to N log M
where: log (2^X) = log (9) is equivalent to the following: X log (2) = log (9)
Since X is multiplied by one term, we will isolate X by performing the opposite operation as what we see.
Isolate the variable X by divididing BOTH sides of equation by log(2):
X log (2) / log (2) = log (9) / log (2) is equivalent to the following: X = log (9) / log (2)
By use of a calculator: X = 3.16992500144
Plug back into original equation to verify that: 2 ^ (3.16992500144) = 9
Although, it may appear complicated at first, but knowing that log is the inverse of exponent and the power/exponent rules it was quickly solved in under 2 mins. The challenge of math comes from forgetting the lower levels of mathematices that come BEFORE the one you are working with. It really does just boil down to the basics...
2^χ=9=>
Log(2^x)=log(9)=>
X*log(2)=log(9)=>
X=log(9)/log(2)=>
X=3.169925