It is nothing about notes, and the teaching methods in these videos show no indication of actually teaching the ideas. For instance - what is the common logarithm of 10? Anyone should see that right away.
I took college algebra twice myself. I made a 69 the first time and cried because I was taking the greyhound to school in a different city. I took college again and made 102 for the course!!!
I’m about to start college at 26 and I am so rusty with my math…but I love math so I’m excited! Will be checking back on this channel for the next few years 😅
@Frank Brown: Your estimate is only for the positive half of the solution: x = ±√10 . Also, you can get a much better approximate: 3 < √10 < 4 because their squares are 9 < 10 < 16 . And you can easily get another digit by writing √10 as √1000/10 and estimate √1000: 31 < √1000 < 32 because 961 < 1000 < 1024 . Thus, 3.1 < √1000/10 < 3.2 . If fact, I know √10 ≈ 3.162277660168379…
95% huh? I know that's just a wild guess of a number to make a point, but the irony of you using the language of statistics to try and say that hardly anyone needs anything beyond basic math is giving me a chuckle.
That’s a complete lie, when I went through engineering, many students started in college algebra, some in lower math courses to build themselves up, there’s no shame in it, but that 95% is so not true and I’d actually say it’s a quite obtuse to make such a preposterous blanket statement.
I was horrible with math in high school. Mainly because I just didn't understand its relevance. Later, as I was introduced to mathematical applications on the job, I came to understand the importance of mathematics. I went to college and successfully completed algebra and trigonometry. Later I completed Calculus I, II, and III along with differential equations, combinatorics, and matrices, and got a degree in Computer Science. It is so important for a teacher to instruct so the student knows the procedures and processes, to recognize the application of mathematics. Especially in high school, students need to be exposed to the power of mathematics, to not see it as a chore but as a challenge. Often, in college, I sought out the answers I needed and worked the problems step by step to understand the solution.
So proud of you!!! Honestly I know that took a lot of work. I was also terrible at math in hs (1st period every year w terrible teachers. Flunked them all) I really hope I can turn the tables this time going back to college and can pass college algebra.
x² = 10 [ x =±√(10) ] 2˟ = 10 [ x = ln(10)/ln(2) ] Honestly, I don't remember covering logarithms in College Algebra. Of course, I took it during the summer where the material was covered at a much faster pace than normal. I do remember covering logarithms in Precalculus and don't ever recall revisiting the material again even after I completed Differential Equations 😊
@@Rudenbehr Calculus tends to use natural logs as the numbers they give are "easier" to handle (and are related to pi and e ) , useful in rotational mechanics and electicity (inc light / radio / audio circuits) for phase / power and similar changes - rotations of dynamos/ motors including frequency syncing and some telecoms systems.
@@RPSchonherr While I have forgotton more about logs than I was ever taught , we had it as "filler" because we had completed the syallabus for the year and slide rules (which are based in part on logs) were going out of use in favour of calculators and I think the cirriculum was dropping the use of log tables at least. So we were shown log tables ( base 10) with the comment that the tables were basically thanks to someone else doing the hard crunching previously but needed still for the addition and finding the anti-log for the result. From memory log10 in base 10 is defined as =1 and thus from that (log100 = 2) the numbers can all be calculated by a form of division. Once we had got the general idea of using log tables for problem solving I decided to create log tables for base 2 , base 5 and base 12 for the fun of it (only the first few natural numbers !!!) cannot remember how to do that (quickly) now
Circa 1988, I was struggling with this stuff in High School Algebra classes. Math was miserable for me. I never got a strong lock on it, and it haunted me later (college) as the math courses moved to Trig, Pre Cal, Cal 1,2,3, and Engineering Math. One MUST have a grasp on the algebra. Now at age 51, I am enjoying these videos, as my mind is waking up and the math is a beautiful mental exercise.
What confused me here was the base of the log 10 and log 2. On my calculator I had to do x=log(10,2)/log(2,2) for the expression to properly solve. Thanks for the walk through, it was very helpful once I learned the bases have to align. 👍
For anyone finding this after the fact: the number in the base actually doesn't matter, as long as it is the same on both sides. In the video they used the common logarithm, or the log to base 10, but any other base also wouldve worked, as long as, again, it is the same on both sides.
Do they still teach analog computing in college? I understand why not used in automotive electronics. To easy to fix and adjust. Part of the design involves solving for a unknown in in fractional power. The analog computer function can also be done with a lot of 1s and 0s. As long as the clock is running in the gigahertz region. It may be just as fast. And as accurate. One method uses digital approximation and the other uses a screwdriver. Both measure and source from analog.
In this example you'd either want to use log(base 2) or log(base 10), or log by default. You can use any base, even e, or natural log (ln) but if I can get one of the figures in the expression to = 1 then I'll use that base. log-base2(2) = 1 log-base10(10) = 1 So, I like: x = logbase2(10) x = 1/log(2)
Well done. You might explain that log 10 = 1, and why that is true. Also that a log IS an exponent. That is, log base b of a is the exponent you have to put on b to get a. For example log 1000 = 3, because 10 cubed is 1000.
I could study, take notes, and do everything right to pass basic algebra, and i would still fail. I am just a moron when it comes to math. I wish that was not the case, but it just is.
0:24 x isn't a "variable" in those equations, it's an unknown. A common mistake if you write code but one that'll you'll definitely get picked up on (at least here in the UK). Also it's a different unknown in each equation; you're just using the same symbol.
@@xl000 Well go and tell my uni lecturers that - they're the ones who mark stuff and this video purports to help you pass academic courses in the subject.
i love love love how you use mathematical terminology like “quadratic equation” or “exponential equation” it makes things so much easier. yesterday was my first day in my college math class and it was essentially a review. and the teacher was just throwing equations up onto the board and he expected us to know already what they were called. and when i asked what type of equation was on the board, he basically told me that it should be general knowledge and i should already know what its called :/ i think that the math class that im in might be too advanced if i can barely keep up and if i cant tell the different between an exp. equation and a quad. equation and especially if i have a teacher not willing to teach me the difference lol
Same my professor starting writing equations etc. and i was clueless on the first day!! I keep thinking i should of reviewed algebra 1, geometry and algebra 2 before college algebra
@@anunknownperson4018 That's gotta feel crazy. Can I ask what class this was? I teach math and I'm trying to get some ideas to be more helpful to my students.
Math experts like to form cliques to try to prove their superiority. This dude refused to answer proving he is more anxious to restrict learning than teaching.
A teacher should not answer like that. With the waste amount of videos today on the internet, you can, as a student, search for these things and get a better understanding. Searching for the right topic, becomes so much easier, if you in fact knows what it is called, the thing you are searching for.
I find that this is so stupid that I need this for my college degree. I’m 41 now and do not understand college algebra and in my field job I would not need this to become HR. This is ridiculous.😊
My basic Problem is that #1 doesn't look like it is solved to me. I was thinking the solution is more like 3.16...... (and a probably endless amount of decimals to get as close as possible to 10. 😬 This is how I always try to figure out algebra and fail time and time again. 🤷🏻♀️
I think of that as testing ones recollection of the two postive AND negative real number solutions for the expression. Calling it a quadratic when effectively it is x^2 +/-0x +/- 0 = 10 is a bit cheeky and also you can use your log tables here for the days when you dont have a babbage machine / calculator / google calc to hand. 2logX=log 10. LogX = (log10)/2 - which you can look up . calculate and then take find the anti log. It would also come up in multiple choice questions with saying for postive solutions in x^2 =10 is X closer to 1, 2, 3, 4 ?. or a question to approximate x to two significant digits or similar kinds of questions.
Brain teasers, brain excercise. Love these simple nibbles. I'm now wanting to do some simple calculus...just for the brain. For anyone who GaF... HP (Moravia) have introduced a new HP15C CE... get them grey cells moving. Best
Technically, a number when contained inside a square root symbol (radical sign) always evaluates as positive. For example, the square root of 4 evaluates to 2, not plus or minus 2. This is so the radical can be used as a function (one output) in different mathematical operations.
I took it 3 times to get a D :) they give you different things to play around with, soon it gets : you making your own numbers and giving them the value you need to call it solved. factoring
My high school desk had large log tables laminated into the top. Graphing calculators were just starting to hit the market, so most of us didn't have one yet, and had to use the handy-dandy table on our desks. :)
Looking at the first one X squared = 10 so X = the square root of 10 which I just happen to remember (from school) is 3.162277 and, of course, it could be + or - The second one is harder .. and I am going to have to watch your video !
Sorry sir but I don't understand you🥲 I'm not gifted of learning since when i was young. But, I have a motivation to learn many things including this matter it is very important to know this, because we can use this in our daily lives. God bless for your trying hard to teach us and for this video. May you continue this♥️
10:35am I have never had Algebra I'm in college and I am behind in my class man I have been trying to understand but I'm not getting it ! Table math has helped me so much ! 😊 Thank you!
I truly wish that I dah an algebra instructor like you when I took high school algebra in 1969. My instructor was a b**ch, (sorry), but she didn't deserve to teach. I diligently tried to take notes, but she criticized me for taking notes and not paying attention. I gradually fell further behind in class until it came to a point where she didn't even call on me. She also failed to tell me that I could have dropped the class to avoid an F grade. Later in high school, I took the same class in summer school and received a B grade, and this instructor at a different high school took his time and thoroughly explained and the class was enjoyable.
All through high school I hated maths until the last year. Up until that last year I’d had sports teachers subbing the maths class that last year I had the head of maths dept and I enjoyed her class and was actually learning unfortunately it was the last year.
Only if they were said to be a "system of equations", but the obvious x=2 result is quickly seen to be extraneous because 2^2 is 4 not 10. If you go back to the beginning of the video, they were said to be two separate problems, therefore X does not represent the same variable. Would have been clearer if it was X^2 = 10 and 2^Z =10
Was so ready to get into college but I just cannot do the math. Would have aced every class except the math. Since I can't develop this skill that I simply will never need in my chosen field, I am locked out. GG WP
But here’s my problem. I’m a quadriplegic (paralyzed neck down) I’m doing online, no actual teacher present, tutors r okay but not the same. Now, most importantly THERES A TIME FRAME! Three assignments do every two days, Monday, Wednesday, Friday. Along with my other classes, no time to step away and breathe and been out of school for 11 years, and the saddest part??? ITS ONLY COLLEGE ALGEBRA! 😔 And I actually like math and solving puzzles/problems but this time limit they have or it’s 10% off your grade each day it’s late is just frustrating. Honestly, don’t want pity just want to find a way to understand
Why has the first equation multiple solutions, while second equation has only one? In fact the second equation has also multiple solutions: Let log be the natural logarithm. Then we have 2^x = e^(xlog2), eaisly verified since log e = 1. But e^(xlog2) = e^(xlog2 + 2PI*i*n), where n = any natural number. Hence we have x = (log10 - 2PI*i*n)/log2 .
took me 8 years to graduate to achieve my associates degree becaue i could never pass the state math college exam. i still dont know how the heck i passed and was able to graduate.
Since those things that are equal to the same thing afre equal to one another then x ^ 2 = 2 ^ x = 10 then again those things.... thus x = 2 appears to be a unique solution. Checking by substitution in the original 2 ^ 2 = 2 ^ 2 but does not equal 10 so there is something wrong with this original asumption and those things equal to the same thing arfe not equal to one another in this situation. Lets look at the individual equations as they have only one unknown and can be solved without reference to the other equation [thus assuming that the unknown x used in both equations may not be the same solution number]. Now using the .equation then x ^ 2 = 10 Lets rename the unknown x as y to avoid confusion of the two conditions of the two equations. Taking logs of both sides [ what you do to one side you do to the other and thus lhs still equals rhs] so that 2.log y = log 10 =1 and thus log y = 1/2 [0.5] thus y = antilog of 2 [cant do this on my phone calculator but appears to be about Using 2 ^ x = 10 [rename x as z for same reasons as above] then do the same to both sides and the equality remains so that 2 ^ z =10 and thus zlog2 =log 10 =1 so that z = 1 divided by log2 = 1/ 0.3010299957 = Not sure if variance in calculator solutions can account for this but then y is almost equal to z [about 3 and a bit] but clearly not equal within 2 decimal places of accuracy] .So my conclusion are that this does not provide a solution using these assumptions and I am tending to consider that if x represents the same quantitiy in both equations then this looks like it can not be solved [at least by me] and indeed i.e. y does not equal z . Just as was demonstrated in my first paragraph " those things equal to the same thing are equal to one another" [ but only if the unknowns x as stated are also the same thing]. So where do we go from here? Are we trying to equate oranges to apples? or is the antilog of 2 = to the log of 10 divided by the log2 ?
I would have misread the question, seeing it as x^2=10, 2^x=10 would be x^2=2^x which means that the original equations solved would be 3.16 and 2.24 respectively and that in this case x^2 not= 2^x. And therefore there is no answer where x^2=2^x=10. x^2=2^x, 2logx=xlog2 which means 2/log2=x/logx, or x=-0.767, x=2, or x=4 and since 2^-0.767=-0.767^2=0.588, 2^2=4 and 4^2=2^4=16, the original premises 2^x=10 and x^2=10 are wrong. Better to have written it as x^2=10, 2^y=10
Upon inspection, I knew the unknown in the 2 equations aren't equal, so he can't be using them as a system of equations. BTW, you're wrong on both parts. x² = 10 x = ±√10 x ≈ ±3.162277660168379… 2^x = 10 x*log(2) = log(10) x = 1/log(2) = log2(10) x ≈ 3.321928094887362…
i’m going to be taking college algebra as i enter ninth grade next year and i am so scared. i flunked algebra pretty hard due to my mental health at the time but currently i’ve been getting the highest grades in geometry throughout my school, but math isn’t something that comes naturally to me but moreover something i study often to help me get to where i need to be. any suggestions before i enter college algebra?
The fact you’re doing it at 9th grade means you’re doing something right 😂. I’m on the same boat where I’m nervous to take it, but honestly learning key words, taking notes about key words and formulas you look over every day seems like a great way to stay ontop of it! Good job you got this!
You kind of messed up the explanation of the positive and negative results from getting the square root of a squared variable. The +/- applied because a number squared would be the same if it were positive or negative. √4 = 2 is correct. If it were √-4, the answer would be 2i. Similarly, √x=2 wouldn't have a +/-, because the variable isn't squared. If x were -4, the number on the right would be 2i as well.
Love your videos, but I I have a small complaint, you mention ‘principal’ values. Please expand on such statements, you went complex w/o giving background. Just give some hints on how much can be explored 🤩
Im resorting to videos because in my math i only got a week before another test is there and we only get grades by tests and not homework and im doing terrible at understanding it because its so fast so this helps
if x^2 is equal to 10 and 2^x is equal to 10 then 2^(x^2=10) equal 10 that means somehow 2^(sqrt 10) equal 10, but that does not equal 10 it is equal 8.95. because sqrt of 10 is 3.162. 2 ^3..235 is equal to 10. . Are these equation exclusive?
I never had high school algebra, it wasn’t required to graduate, just one year of general math was all that was required. I’ve sucked at math since the first time I had math in whatever grade that was, it’s been so long now. Probably why I only have 48 semester hours of college I was afraid I wouldn’t pass college level math. But that’s okay. College is overrated. I worked hard to get own my own house, 2 cars, a Harley, a pool, a descent savings and two full time careers both with good monthly pensions and a social security checks. I’m happily married and content. At 67 and retired I may try the college thing again, if there is college algebra involved, we’ll, I’ll tackle that when it comes.
Also, what is considered taking good notes? Cause I’m flat out just horrible taking notes. I never had a proper education. I’m waiting to that, but I’m also waiting to admit that even though it’s 11 years later, I want to change these habits just didn’t think it’d be this hard (taking notes)
Calculater? I am too old. I was not even allowd a slide rule. Had to use log tables. England and Scotland still have adder snakes; but not Ireland. The Scots and Brits built sturdy tables out of logs so that the adders could multiply. ;-)
Really? log10/log2?? You didn't then go, and since log10 (assuming base of 10, which you can define when taking the initial logs) is 1, the answer is 1/log2
I passed with a D in algebra 1 and a b in geometry. I haven't taken any math classes since now I am starting college and I don't think I can pass any of it. I don't understand any of this and I just can't seem to grasp it.
My advice is to take all your general education courses and major courses that do not require a math prerequisite first. Once you've got those out of the way then you can devote more time to your math requirement. I suggest pick a math class that you feel comfortable taking and buy a used textbook for that course and study for it by watching RUclips tutorials or tutoring before you pay to take the class. Once you got it down only then should you enroll in the class and you shouldn't have a hard time getting by with a "C" ( passing grade).
The topics in this video might not be a good start for you, but I bet you can still do it. I want to help people just like you and I'm working on videos to help. Do you mind answering some questions so I have a better idea of how to help? Don't give up.
The guessing for the second one is actually a good idea to check your precise answer makes sense. But why not just say it ends up as one over log2 and give the actual result?
log(x) is typically defined as the logarithm function, base 10, but it can be used for an unspecified base. When the base is e, the function is commonly written as ln(x), the natural logarithm. In the generic form of log(x), the solution for 2^x=10 is log(10)/log(2), which works for any base, be it 10, e, 2, 3, etc. This form also translates to log2(10).
before a clicked on the video (only saw the thumbnail)i thought the question is which is bigger sqrt(10) or log2(10) and why.... im disappointed that was not the topic, i thought we were going to see a algebraic solution for that
I’m in 6th grade, bored, because of that boredom I now know, algebra one, algebra two, college algebra, the Pythagorean theorem , calculus, around 100 digits of pi, and is now at 12th grade for reading, so, moral of the story be bored.
You write down the multiply symbol and you "see" the addition symbol. Perhaps you should learn what the symbols actually mean rather than just what you "see".
I could never understand math in school, rote education doesn't work for me. I bought the books, watched videos and practiced with paper and pencil, various problems, until i understood the subject. I finely completed polynomial algebra and have no need or desire to go further but i know i can if need be. Sometimes one has to figure out what tools one needs to learn the subject first, school isn't appropriate for everyone.
I flunked calculus 1 in 1969. I’ve promised myself for 50+ years that I’d get back on the horse what throwed me, but I think I’m too old.. Wish I had the money to hire a tutor.
the problem that I had with algebra was that it wasn't enough to get the right answer. You also had to show your work. I could give you the answer but not show you how I arrived at that answer.
It used to be that students would learn algebra in middle school! Yet our American dictatorship decided that it is not profitable for students to learn algebra for free! Therefore, they strongly encourage students to wait until paid college to learn things like algebra! The truth is that they don't want anyone here to know very much, and if you do, then you will be severely punished!
It takes a good teacher to make sure students understand the process. Its not all about notes but patience & attention to students.
It is nothing about notes, and the teaching methods in these videos show no indication of actually teaching the ideas. For instance - what is the common logarithm of 10? Anyone should see that right away.
I’m gonna try college algebra for the 4th time and I’m 40 so I’m hoping this is my last time wasting money on remedial classes 😅
I took college algebra twice myself. I made a 69 the first time and cried because I was taking the greyhound to school in a different city. I took college again and made 102 for the course!!!
May be that you need to start out by reviewing basic math and algebra first 🤷♂️
Congrats on making that decision! My brother had the same issues with doing remedial classes over and over again. You can definitely do it!
@@btbmath1229 thanks my dude
@@captaingreatvalue3176 I teach remedial classes. Can I ask is there anything you wish the teachers would do to help you more?
I’m about to start college at 26 and I am so rusty with my math…but I love math so I’m excited! Will be checking back on this channel for the next few years 😅
Good luck in college! You got this!
@@Chloe-tz3kw Thanks :) Khan Academy is suuuper helpful.
Aww how funny! I’m 26 and starting college this fall. Taking college algebra. I’m considering tutoring as well.
@@Aniexo_ Good luck :) What is your major?
Don't worry. The solution is not dependent on being in a certain college class or not. Mathematics is mathematics. You will do well. Have fun!
Thanks a lot, great to bring back old memories, 72 yrs old Mechanical Engineer with a Master Thesis in Calculus.,
what kind of master's is in calculus? that's uni or highschool where I am at. Do you mean analysis?
Oh wow...much respect to you sir, that's an impressive skill set!
Were you born in 1950?
1Q. X= + or -- square root of 10 which is between 3 and 5
2Q X = 1/ log(2)
@Frank Brown: Your estimate is only for the positive half of the solution: x = ±√10 . Also, you can get a much better approximate: 3 < √10 < 4 because their squares are 9 < 10 < 16 . And you can easily get another digit by writing √10 as √1000/10 and estimate √1000: 31 < √1000 < 32 because 961 < 1000 < 1024 . Thus, 3.1 < √1000/10 < 3.2 . If fact, I know √10 ≈ 3.162277660168379…
Ahh the reason 95% of people who wanted to go to college end up not going, myself included.
Yea it suck cuz I gotta take trig n calculus for my degree
Fortunately 95% of students do not need this level of math. What they do need is a excellent knowledge of basic math.
95% huh? I know that's just a wild guess of a number to make a point, but the irony of you using the language of statistics to try and say that hardly anyone needs anything beyond basic math is giving me a chuckle.
That’s a complete lie, when I went through engineering, many students started in college algebra, some in lower math courses to build themselves up, there’s no shame in it, but that 95% is so not true and I’d actually say it’s a quite obtuse to make such a preposterous blanket statement.
This isn't even close to basic math.
It's prep for the course you need to take in prep for basic math.
@@Lemuraiit obviously depends on what major you’re pursuing 🙄
Agreed
I was horrible with math in high school. Mainly because I just didn't understand its relevance. Later, as I was introduced to mathematical applications on the job, I came to understand the importance of mathematics. I went to college and successfully completed algebra and trigonometry. Later I completed Calculus I, II, and III along with differential equations, combinatorics, and matrices, and got a degree in Computer Science.
It is so important for a teacher to instruct so the student knows the procedures and processes, to recognize the application of mathematics. Especially in high school, students need to be exposed to the power of mathematics, to not see it as a chore but as a challenge. Often, in college, I sought out the answers I needed and worked the problems step by step to understand the solution.
That was big-headed of you 😅
So proud of you!!! Honestly I know that took a lot of work. I was also terrible at math in hs (1st period every year w terrible teachers. Flunked them all) I really hope I can turn the tables this time going back to college and can pass college algebra.
Your story is great and also proves that just because you don't do good at something in high school you can't get better at it..
@@cynthiapuma3299good luck to you I wish you all the luck in the world.. and you can do it 👍
For those of us who wrote assembly language the rule of thumb was 3 1/3 bits per decimal digit. So log 10/log 2 ~ 3.3
OK but it applies to all languages.
x² = 10 [ x =±√(10) ]
2˟ = 10 [ x = ln(10)/ln(2) ]
Honestly, I don't remember covering logarithms in College Algebra. Of course, I took it during the summer where the material was covered at a much faster pace than normal.
I do remember covering logarithms in Precalculus and don't ever recall revisiting the material again even after I completed Differential Equations 😊
I remember because I asked the instructor how do we calculate logs and he didn't know. "Just use the tables," was his answer.
Same experience too. Common logs covered extensively in algebra. But calculus seemed to just use natural log.
@@Rudenbehr Calculus tends to use natural logs as the numbers they give are "easier" to handle (and are related to pi and e ) , useful in rotational mechanics and electicity (inc light / radio / audio circuits) for phase / power and similar changes - rotations of dynamos/ motors including frequency syncing and some telecoms systems.
@@RPSchonherr While I have forgotton more about logs than I was ever taught , we had it as "filler" because we had completed the syallabus for the year and slide rules (which are based in part on logs) were going out of use in favour of calculators and I think the cirriculum was dropping the use of log tables at least. So we were shown log tables ( base 10) with the comment that the tables were basically thanks to someone else doing the hard crunching previously but needed still for the addition and finding the anti-log for the result. From memory log10 in base 10 is defined as =1 and thus from that (log100 = 2) the numbers can all be calculated by a form of division. Once we had got the general idea of using log tables for problem solving I decided to create log tables for base 2 , base 5 and base 12 for the fun of it (only the first few natural numbers !!!) cannot remember how to do that (quickly) now
I remember using my log book before the days of calculator.
Circa 1988, I was struggling with this stuff in High School Algebra classes. Math was miserable for me. I never got a strong lock on it, and it haunted me later (college) as the math courses moved to Trig, Pre Cal, Cal 1,2,3, and Engineering Math. One MUST have a grasp on the algebra. Now at age 51, I am enjoying these videos, as my mind is waking up and the math is a beautiful mental exercise.
I struggle with math and this has been extremely helpful. I am committed to know moore on college algebra.
I passed college algebra in 2004 and had no idea how to solve this.
What confused me here was the base of the log 10 and log 2. On my calculator I had to do x=log(10,2)/log(2,2) for the expression to properly solve. Thanks for the walk through, it was very helpful once I learned the bases have to align. 👍
For anyone finding this after the fact: the number in the base actually doesn't matter, as long as it is the same on both sides. In the video they used the common logarithm, or the log to base 10, but any other base also wouldve worked, as long as, again, it is the same on both sides.
Do they still teach analog computing in college? I understand why not used in automotive electronics. To easy to fix and adjust.
Part of the design involves solving for a unknown in in fractional power.
The analog computer function can also be done with a lot of 1s and 0s.
As long as the clock is running in the gigahertz region. It may be just as fast. And as accurate.
One method uses digital approximation and the other uses a screwdriver. Both measure and source from analog.
Just use e as the base
In this example you'd either want to use log(base 2) or log(base 10), or log by default. You can use any base, even e, or natural log (ln) but if I can get one of the figures in the expression to = 1 then I'll use that base.
log-base2(2) = 1
log-base10(10) = 1
So, I like:
x = logbase2(10)
x = 1/log(2)
Just use natural log and you don’t have to worry about the base
I am about to start a college algebra class next week, definitely need this
Good luck 👍
@@ralphmelvin1046 thanks
Well done. You might explain that log 10 = 1, and why that is true.
Also that a log IS an exponent. That is, log base b of a is the exponent you have to put on b to get a.
For example log 1000 = 3, because 10 cubed is 1000.
Logarithm is the inverse operation of exponentiation
Here is how to do so:
Take natural logarithm of both sides of the 2nd eq gives:
ln 2^x = ln10 -----> x = ln10 / ln 2
You're done
I could study, take notes, and do everything right to pass basic algebra, and i would still fail. I am just a moron when it comes to math. I wish that was not the case, but it just is.
same, already lost halfway into this video, took the class twice
I'm really good in basic math but algebra leaves me confused 🤔
0:24 x isn't a "variable" in those equations, it's an unknown. A common mistake if you write code but one that'll you'll definitely get picked up on (at least here in the UK). Also it's a different unknown in each equation; you're just using the same symbol.
This is nitpicking
@@xl000 Well go and tell my uni lecturers that - they're the ones who mark stuff and this video purports to help you pass academic courses in the subject.
Thank you 🙏
x is a variable in each equation.also it's pretty obvious they are separate equations, so using x in both is not confusing!
In USA, AN UNKNOWN IS A VARIABLE!
Excellent demonstration Sir !
Fortunately, I was able to substitute two years of Latin for 1 year of math in college. I enjoyed Latin.
i love love love how you use mathematical terminology like “quadratic equation” or “exponential equation” it makes things so much easier.
yesterday was my first day in my college math class and it was essentially a review. and the teacher was just throwing equations up onto the board and he expected us to know already what they were called. and when i asked what type of equation was on the board, he basically told me that it should be general knowledge and i should already know what its called :/
i think that the math class that im in might be too advanced if i can barely keep up and if i cant tell the different between an exp. equation and a quad. equation
and especially if i have a teacher not willing to teach me the difference lol
Same my professor starting writing equations etc. and i was clueless on the first day!! I keep thinking i should of reviewed algebra 1, geometry and algebra 2 before college algebra
@@anunknownperson4018 That's gotta feel crazy. Can I ask what class this was? I teach math and I'm trying to get some ideas to be more helpful to my students.
average fucking loser math teacher with a big ass ego
Math experts like to form cliques to try to prove their superiority. This dude refused to answer proving he is more anxious to restrict learning than teaching.
A teacher should not answer like that. With the waste amount of videos today on the internet, you can, as a student, search for these things and get a better understanding. Searching for the right topic, becomes so much easier, if you in fact knows what it is called, the thing you are searching for.
I find that this is so stupid that I need this for my college degree. I’m 41 now and do not understand college algebra and in my field job I would not need this to become HR. This is ridiculous.😊
My basic Problem is that #1 doesn't look like it is solved to me. I was thinking the solution is more like 3.16...... (and a probably endless amount of decimals to get as close as possible to 10. 😬 This is how I always try to figure out algebra and fail time and time again. 🤷🏻♀️
I think of that as testing ones recollection of the two postive AND negative real number solutions for the expression. Calling it a quadratic when effectively it is x^2 +/-0x +/- 0 = 10 is a bit cheeky and also you can use your log tables here for the days when you dont have a babbage machine / calculator / google calc to hand. 2logX=log 10. LogX = (log10)/2 - which you can look up . calculate and then take find the anti log. It would also come up in multiple choice questions with saying for postive solutions in x^2 =10 is X closer to 1, 2, 3, 4 ?. or a question to approximate x to two significant digits or similar kinds of questions.
Brain teasers, brain excercise. Love these simple nibbles. I'm now wanting to do some simple calculus...just for the brain.
For anyone who GaF... HP (Moravia) have introduced a new HP15C CE... get them grey cells moving.
Best
Technically, a number when contained inside a square root symbol (radical sign) always evaluates as positive. For example, the square root of 4 evaluates to 2, not plus or minus 2. This is so the radical can be used as a function (one output) in different mathematical operations.
This presentation is excellent and brought back many enjoyable memories of my algebra classes.
If using base 10, log(10) = 1, so you can simplify as x = 1/log (2)
X^2 = 10 square root each side X =+/- SQRT(10)
My genious son helped me pass college algebra, but this guy is a good teacher if anyone needs help!
for the exponential equation the simple answer is x=(log(2))^-1. (log(10) =1)
Amazing teacher-love your style! Thank you!
I took it 3 times to get a D :) they give you different things to play around with, soon it gets : you making your own numbers and giving them the value you need to call it solved. factoring
The first two minutes brought back my worst memories of HS. Giving up on math 50 yrs ago was the right choice.
Love your channel it’s incredibly helpful
x = + or - sqrt(10) and x = log(10)/log(2). Does not matter base of the log as long as they are the same.
My high school desk had large log tables laminated into the top. Graphing calculators were just starting to hit the market, so most of us didn't have one yet, and had to use the handy-dandy table on our desks. :)
Looking at the first one X squared = 10 so X = the square root of 10
which I just happen to remember (from school) is 3.162277
and, of course, it could be + or -
The second one is harder .. and I am going to have to watch your video !
Been out if college over 40yrs... And this was good. Didnt have anything like this. 😮 thank you.
since log10=1, the solution is 1/log2 about 3.32
Sorry sir but I don't understand you🥲 I'm not gifted of learning since when i was young. But, I have a motivation to learn many things including this matter it is very important to know this, because we can use this in our daily lives. God bless for your trying hard to teach us and for this video. May you continue this♥️
10:35am I have never had Algebra I'm in college and I am behind in my class man I have been trying to understand but I'm not getting it ! Table math has helped me so much ! 😊 Thank you!
Great overview my man.
Appreciate the help I really need this
I truly wish that I dah an algebra instructor like you when I took high school algebra in 1969. My instructor was a b**ch, (sorry), but she didn't deserve to teach. I diligently tried to take notes, but she criticized me for taking notes and not paying attention. I gradually fell further behind in class until it came to a point where she didn't even call on me. She also failed to tell me that I could have dropped the class to avoid an F grade. Later in high school, I took the same class in summer school and received a B grade, and this instructor at a different high school took his time and thoroughly explained and the class was enjoyable.
All through high school I hated maths until the last year. Up until that last year I’d had sports teachers subbing the maths class that last year I had the head of maths dept and I enjoyed her class and was actually learning unfortunately it was the last year.
Cool tp see howamy people relates to matj, specially the older people. Lord bless you all!!!
The only thing i got out of algebra was a migraine ...............
there are two elements that are both equal to 10. Therefore they are equal to each other as well.
Only if they were said to be a "system of equations", but the obvious x=2 result is quickly seen to be extraneous because 2^2 is 4 not 10.
If you go back to the beginning of the video, they were said to be two separate problems, therefore X does not represent the same variable. Would have been clearer if it was X^2 = 10 and 2^Z =10
Why don’t you find the square root of 10 then right that down with plus or minus?
You can use a calculator for a good approximation.
Was so ready to get into college but I just cannot do the math. Would have aced every class except the math. Since I can't develop this skill that I simply will never need in my chosen field, I am locked out. GG WP
But here’s my problem. I’m a quadriplegic (paralyzed neck down) I’m doing online, no actual teacher present, tutors r okay but not the same. Now, most importantly THERES A TIME FRAME! Three assignments do every two days, Monday, Wednesday, Friday. Along with my other classes, no time to step away and breathe and been out of school for 11 years, and the saddest part??? ITS ONLY COLLEGE ALGEBRA! 😔 And I actually like math and solving puzzles/problems but this time limit they have or it’s 10% off your grade each day it’s late is just frustrating.
Honestly, don’t want pity just want to find a way to understand
Why has the first equation multiple solutions, while second equation has only one? In fact the second equation has also multiple solutions: Let log be the natural logarithm. Then we have 2^x = e^(xlog2), eaisly verified since log e = 1. But e^(xlog2) = e^(xlog2 + 2PI*i*n), where n = any natural number. Hence we have x = (log10 - 2PI*i*n)/log2 .
4:56: Wrong. If you take √4, the answer is only 2, not - 2. If you take ± √4, the answer is ± 2.
It's correct -2 X -2 also = 4 Two negatives multiplied make a positive.
@@67Pepper Yes. But that doesn’t change the fact that the principle root is non-negative.
I guess my question would be an example of where this would be useful in life and how it would be used
took me 8 years to graduate to achieve my associates degree becaue i could never pass the state math college exam. i still dont know how the heck i passed and was able to graduate.
Since those things that are equal to the same thing afre equal to one another then x ^ 2 = 2 ^ x = 10 then again those things.... thus x = 2 appears to be a unique solution. Checking by substitution in the original 2 ^ 2 = 2 ^ 2 but does not equal 10 so there is something wrong with this original asumption and those things equal to the same thing arfe not equal to one another in this situation.
Lets look at the individual equations as they have only one unknown and can be solved without reference to the other equation [thus assuming that the unknown x used in both equations may not be the same solution number].
Now using the .equation then x ^ 2 = 10 Lets rename the unknown x as y to avoid confusion of the two conditions of the two equations. Taking logs of both sides [ what you do to one side you do to the other and thus lhs still equals rhs] so that 2.log y = log 10 =1 and thus log y = 1/2 [0.5] thus y = antilog of 2 [cant do this on my phone calculator but appears to be about
Using 2 ^ x = 10 [rename x as z for same reasons as above] then do the same to both sides and the equality remains so that 2 ^ z =10 and thus zlog2 =log 10 =1 so that z = 1 divided by log2 = 1/ 0.3010299957 =
Not sure if variance in calculator solutions can account for this but then y is almost equal to z [about 3 and a bit] but clearly not equal within 2 decimal places of accuracy] .So my conclusion are that this does not provide a solution using these assumptions and I am tending to consider that if x represents the same quantitiy in both equations then this looks like it can not be solved [at least by me] and indeed i.e. y does not equal z .
Just as was demonstrated in my first paragraph " those things equal to the same thing are equal to one another" [ but only if the unknowns x as stated are also the same thing]. So where do we go from here? Are we trying to equate oranges to apples? or is the antilog of 2 = to the log of 10 divided by the log2 ?
You can put log base 2 of 10 in most scientific calculators
did not need both expressions to solve . each one was solvable .
I would have misread the question, seeing it as x^2=10, 2^x=10 would be x^2=2^x which means that the original equations solved would be 3.16 and 2.24 respectively and that in this case x^2 not= 2^x. And therefore there is no answer where x^2=2^x=10.
x^2=2^x, 2logx=xlog2 which means 2/log2=x/logx, or x=-0.767, x=2, or x=4 and since 2^-0.767=-0.767^2=0.588, 2^2=4 and 4^2=2^4=16, the original premises 2^x=10 and x^2=10 are wrong.
Better to have written it as x^2=10, 2^y=10
Upon inspection, I knew the unknown in the 2 equations aren't equal, so he can't be using them as a system of equations.
BTW, you're wrong on both parts.
x² = 10
x = ±√10
x ≈ ±3.162277660168379…
2^x = 10
x*log(2) = log(10)
x = 1/log(2) = log2(10)
x ≈ 3.321928094887362…
Pop goes the weasel song to remember the quadratic formula..y=-b+-sqrrt of 4ab/2a
Is log10=1? When I was learning this stuff, there was no calculator. We had to look up the tables or draw a chart.
i’m going to be taking college algebra as i enter ninth grade next year and i am so scared. i flunked algebra pretty hard due to my mental health at the time but currently i’ve been getting the highest grades in geometry throughout my school, but math isn’t something that comes naturally to me but moreover something i study often to help me get to where i need to be. any suggestions before i enter college algebra?
The fact you’re doing it at 9th grade means you’re doing something right 😂. I’m on the same boat where I’m nervous to take it, but honestly learning key words, taking notes about key words and formulas you look over every day seems like a great way to stay ontop of it! Good job you got this!
Trig.
4 minutes 40 seconds in and still no equation steps shown/completed? I think this is far too drawn out.
figure its pretty obvious that its the Square Root of 10 (ie, 10^0.5) which is roughly 3.16
Important matter for us and thank you !
You kind of messed up the explanation of the positive and negative results from getting the square root of a squared variable. The +/- applied because a number squared would be the same if it were positive or negative. √4 = 2 is correct. If it were √-4, the answer would be 2i. Similarly, √x=2 wouldn't have a +/-, because the variable isn't squared. If x were -4, the number on the right would be 2i as well.
Quadratic equations have
Two solutions.
X*x=0
or just one solution...
Love your videos, but I I have a small complaint, you mention ‘principal’ values. Please expand on such statements, you went complex w/o giving background. Just give some hints on how much can be explored 🤩
+- √10 is redundant since √10 has +- solutions. I would just say X = √10
X=10^½, 2=10^(1/x)
Im resorting to videos because in my math i only got a week before another test is there and we only get grades by tests and not homework and im doing terrible at understanding it because its so fast so this helps
Im studying my ass off cause I need to do well on this test tomorrow
if x^2 is equal to 10 and 2^x is equal to 10 then 2^(x^2=10) equal 10 that means somehow 2^(sqrt 10) equal 10, but that does not equal 10 it is equal 8.95. because sqrt of 10 is 3.162. 2 ^3..235 is equal to 10. . Are these equation exclusive?
I never had high school algebra, it wasn’t required to graduate, just one year of general math was all that was required. I’ve sucked at math since the first time I had math in whatever grade that was, it’s been so long now. Probably why I only have 48 semester hours of college I was afraid I wouldn’t pass college level math.
But that’s okay. College is overrated. I worked hard to get own my own house, 2 cars, a Harley, a pool, a descent savings and two full time careers both with good monthly pensions and a social security checks. I’m happily married and content.
At 67 and retired I may try the college thing again, if there is college algebra involved, we’ll, I’ll tackle that when it comes.
Get,s into the problems at 2:53
Also, what is considered taking good notes? Cause I’m flat out just horrible taking notes. I never had a proper education. I’m waiting to that, but I’m also waiting to admit that even though it’s 11 years later, I want to change these habits just didn’t think it’d be this hard (taking notes)
Calculater? I am too old. I was not even allowd a slide rule. Had to use log tables. England and Scotland still have adder snakes; but not Ireland. The Scots and Brits built sturdy tables out of logs so that the adders could multiply. ;-)
Really? log10/log2?? You didn't then go, and since log10 (assuming base of 10, which you can define when taking the initial logs) is 1, the answer is 1/log2
The only solution that satisfies both equations is the positive x value.
I passed with a D in algebra 1 and a b in geometry. I haven't taken any math classes since now I am starting college and I don't think I can pass any of it. I don't understand any of this and I just can't seem to grasp it.
My advice is to take all your general education courses and major courses that do not require a math prerequisite first. Once you've got those out of the way then you can devote more time to your math requirement. I suggest pick a math class that you feel comfortable taking and buy a used textbook for that course and study for it by watching RUclips tutorials or tutoring before you pay to take the class. Once you got it down only then should you enroll in the class and you shouldn't have a hard time getting by with a "C" ( passing grade).
The topics in this video might not be a good start for you, but I bet you can still do it. I want to help people just like you and I'm working on videos to help. Do you mind answering some questions so I have a better idea of how to help? Don't give up.
@@btbmath1229 I don't mind answering questions
Kod mene zadatak drugi je nedovršen jer treba uvažiti da log ima bazu 10 i da je log10=1, pa je konačni rezultat x=1/(log2).
Just subscribed! Love your work!
X = log_2(10)
You used X twice, which could imply the two equations are related.
The guessing for the second one is actually a good idea to check your precise answer makes sense. But why not just say it ends up as one over log2 and give the actual result?
log(x) is typically defined as the logarithm function, base 10, but it can be used for an unspecified base. When the base is e, the function is commonly written as ln(x), the natural logarithm. In the generic form of log(x), the solution for 2^x=10 is log(10)/log(2), which works for any base, be it 10, e, 2, 3, etc. This form also translates to log2(10).
before a clicked on the video (only saw the thumbnail)i thought the question is which is bigger sqrt(10) or log2(10) and why.... im disappointed that was not the topic, i thought we were going to see a algebraic solution for that
Well done John.
I’m in 6th grade, bored, because of that boredom I now know, algebra one, algebra two, college algebra, the Pythagorean theorem , calculus, around 100 digits of pi, and is now at 12th grade for reading, so, moral of the story be bored.
Hold on how did you get 8 from 2x2x2? Im seeing 6. And then 2x2x2x2=16? I'm seeing 8.
You'll get 6 when you add 2+2+2.
Youll get 8 when you multiply 2 times 2 times 2.
You write down the multiply symbol and you "see" the addition symbol.
Perhaps you should learn what the symbols actually mean rather than just what you "see".
2 times 2 is 4 and then 4 times 2 is 8
I could never understand math in school, rote education doesn't work for me. I bought the books, watched videos and practiced with paper and pencil, various problems, until i understood the subject.
I finely completed polynomial algebra and have no need or desire to go further but i know i can if need be. Sometimes one has to figure out what tools one needs to learn the subject first, school isn't appropriate for everyone.
I flunked calculus 1 in 1969. I’ve promised myself for 50+ years that I’d get back on the horse what throwed me, but I think I’m too old.. Wish I had the money to hire a tutor.
the problem that I had with algebra was that it wasn't enough to get the right answer. You also had to show your work. I could give you the answer but not show you how I arrived at that answer.
Quadratic equations don’t always have 2 answers
One is a factor and the other is a logarithm.
It used to be that students would learn algebra in middle school! Yet our American dictatorship decided that it is not profitable for students to learn algebra for free! Therefore, they strongly encourage students to wait until paid college to learn things like algebra! The truth is that they don't want anyone here to know very much, and if you do, then you will be severely punished!
Can you explain WHY? My algebra teacher in high school couldn't.
I’m lost as hell and not excited to take math this semester 😢 English major
huh? 10 = 2 ^x => x = ln base 2 of 10 ... which is the same answer
im still lost. idk if im ever going to understand alegbra i have a proficiency intermedite alegbra test and i already failed the basic math one
the best book to learn algebra is ALGEBRA OF BALDOR try to find it in english version
x^2 = 10 = 2^x seems to imply that x^2 = 2^x so x = 2. The 10 is superfluous?
No, he wrote separate equations that look similar, but are really different.