I believe, that irrespective of those who teach Math and claim that with good instruction in Math, most can learn it. The fact still remains that we ALL have different gifts and talents. Some are naturally drawn to Science, some to the Arts, some to neither and do whatever to survive. The teaching in Math in my era (1950's) was abysmal. They sorted us out into those who were good at Math and put the rest of us to one side and concentrated on those who were the stars in Math, Science etc, while the rest of us who mostly were creative were looked down upon with disain. But I am happy being who I am. However, having said the above, I still try my best to understand the concepts of a subject I struggled with at school, still trying to understand the basic principles of Algebra, Geometry and Trigonometry. I have improved substantially in Math, thanks to this website! Thank God for John's instructions, I have learn't a lot from him. Thank you John! I am still trying to get there , now in my 70s'! lol!❤👍
In that era the 19th century educational model was geared toward cataloging people and moving them through the system. Even in the 20th century, at that time there was no other choice. The size of a classroom had to be small enough so the teacher could talk in a normal voice and still be heard by all students in the room. This limited the size of a classroom to accommodate 30 desks and 30 students. To prevent the school resources from being overwhelmed by the number of students, the concept of grades had to be used to flush people through the process whether of not they understood all of the coursework.. A student receiving a B (80%) shows that they failed to understand 20% of the course material. Instead of making sure the student understood the 20% they missed, it was more expedient to catalog them as a good student and move them to the next level. Now, in the 21st century we have computers and the internet. Instead of 30 students in a classroom, with a teacher repeating the same lecture hour after hour, day after day, a teacher can record the lecture in an instructional video only once and reach millions of students. A student now has the ability to review the video as many times as necessary to understand the material. If necessary, the student can pause the instruction to gain any background information that may be required to understand the subject. Once 100% of the material is understood it is time to move to the next level of instruction. Some will move to the next level faster than others, but grades should no longer be used to indicate a person's usefulness. They should only be used to indicate that additional study is needed to understand a subject. . The technology now exists to educate, instead of catalog and make education available to all who want to learn.
Got 2.7 by sight. Then played with the calc. Thanks for the fun. I remember log tables in the back of the book. Graduated high school in 69. Never had the opportunity to learn a slide rule. Shame, they are awesome.
Why didn’t you do a log? You always get close to answer but you also seem to got distracted and rarely finish with complete instruction. You should mentioning what you do plan to do. It can confused the learner.
I think that the value of the ratio here [ (log20)/(log3)) ] will remain constant regardless the value that the bases have, assuming that the bases are the same. This allows the expression to be written as "log 20 base 3". .. (note that log a base a = 1).
To solve 3x=203^x = 20, you can use logarithms. Here's the step-by-step process: Start with the equation: 3x=203^x = 20 Take the natural logarithm (ln\ln) on both sides: ln(3x)=ln(20)\ln(3^x) = \ln(20) Use the power rule of logarithms (ln(ab)=bln(a)\ln(a^b) = b \ln(a)): xln(3)=ln(20)x \ln(3) = \ln(20) Solve for xx: x=ln(20)ln(3)x = \frac{\ln(20)}{\ln(3)} Calculate the result using a calculator: x≈2.99571.0986≈2.73x \approx \frac{2.9957}{1.0986} \approx 2.73 So, x≈2.73x \approx 2.73. This approach works for exponential equations that don’t have integer solutions. Tools like SolutionInn's AI study aids can make equations like this easier to master by offering step-by-step explanations and plenty of practice problems tailored to your needs.
I have to wonder why your video (and many similar videos on this type of problem) use the log rule that log 3^x = x log 3 when a much simpler procedure is to take log base 3 of 3^x and log base 3 of 20. Then you have x = log base 3 of 20 = ln 20/ln 3, which gives the same answer and is so much quicker. And it can be quickly computed on a calculator.
I remember in High-School (1961-1964) there was a course called Confucian, a sort of high school advanced Algebra / Calculus course that had log tables at the end of the book. I even remember there was a complete book of log tables. I also, for some reason, bought a Picket Slide Rule and even had some vague idea of how to use it. I bought that sometime in the late 60s and still have it, complete with stiff leather holder. In the end, I thought Math presented an awful lot of work for very small results. And Literature was far more practical.
I understood the method presented to solve for x by logs but I’m confused about x=2.72 in the first place. So, 3^2 is 3*3, and 3^3 is 3*3*3. That’s seems clear because I see the exp. is the number of times the base value is multiplied by itself. But 3^2.72 ? It’s not 3*3*(3*0.72) as this isn’t nearly equal to 20. If x = 2.74, and 3^2.74 = 3*3*(3*0.74), that would be closer to 20. So I don’t get it fundamentally.
Using trial and error a number of times, you can get: 2.726833 But logs are easier because log(20) / log(3) = 2.726833 perfect! For those wanting a bit of history, engineers and scientists used to do it the same way with a slide rule.
15:10 You're going to need Log Tables, a slide rule OR a calculator! We had a demonstration slide rule hanging on the wall by the blackboard, about 5' long, that the professor used to teach our class how to use them. I wonder where all those went? A museum?
When I took Trigonometry and Algebra II, I had to use a slide rule. I think I still have a slide rule. I heard it can be done on an abacus, but I don't know how.
In 1972 I competed in UIL drama and poetry interpretation (get the picture of my expertise?) My math teacher asked me to sign up for slide rule because the school got points for entrants regardless of how they did. I was actually a little proud of myself for coming in 11th out of 12 entrants because I didn't come in last.
To get the answer. Get the log and the lookup the log in a log table... Tbh logarithms are such an idiotic thing. A relic from the past to make calculations more efficient that really shouldn't be around anymore
How difficult would it be to show this on an actual calculator? Does RUclips pay you by the time you waste from your poor viewers? You could have done 10 examples instead of running memory sad lane. Are you teaching math, or history? English you could not teach to save your life. Invest in a remedial class.
I believe, that irrespective of those who teach Math and claim that with good instruction in Math, most can learn it. The fact still remains that we ALL have different gifts and talents. Some are naturally drawn to Science, some to the Arts, some to neither and do whatever to survive. The teaching in Math in my era (1950's) was abysmal. They sorted us out into those who were good at Math and put the rest of us to one side and concentrated on those who were the stars in Math, Science etc, while the rest of us who mostly were creative were looked down upon with disain. But I am happy being who I am. However, having said the above, I still try my best to understand the concepts of a subject I struggled with at school, still trying to understand the basic principles of Algebra, Geometry and Trigonometry. I have improved substantially in Math, thanks to this website! Thank God for John's instructions, I have learn't a lot from him. Thank you John! I am still trying to get there , now in my 70s'! lol!❤👍
I agree with you word to word Treva
In that era the 19th century educational model was geared toward cataloging people and moving them through the system. Even in the 20th century, at that time there was no other choice. The size of a classroom had to be small enough so the teacher could talk in a normal voice and still be heard by all students in the room. This limited the size of a classroom to accommodate 30 desks and 30 students. To prevent the school resources from being overwhelmed by the number of students, the concept of grades had to be used to flush people through the process whether of not they understood all of the coursework.. A student receiving a B (80%) shows that they failed to understand 20% of the course material. Instead of making sure the student understood the 20% they missed, it was more expedient to catalog them as a good student and move them to the next level. Now, in the 21st century we have computers and the internet. Instead of 30 students in a classroom, with a teacher repeating the same lecture hour after hour, day after day, a teacher can record the lecture in an instructional video only once and reach millions of students. A student now has the ability to review the video as many times as necessary to understand the material. If necessary, the student can pause the instruction to gain any background information that may be required to understand the subject. Once 100% of the material is understood it is time to move to the next level of instruction. Some will move to the next level faster than others, but grades should no longer be used to indicate a person's usefulness. They should only be used to indicate that additional study is needed to understand a subject. . The technology now exists to educate, instead of catalog and make education available to all who want to learn.
Got 2.7 by sight.
Then played with the calc.
Thanks for the fun.
I remember log tables in the back of the book.
Graduated high school in 69.
Never had the opportunity to learn a slide rule.
Shame, they are awesome.
Greetings.
3^x=20,
Log 3^x=Log20,
X Log 3=Log20,
XLog3/Log3=
Log20/Log3,
X=Log20/Log3,
X=Log 20 base 3.
Why didn’t you do a log? You always get close to answer but you also seem to got distracted and rarely finish with complete instruction. You should mentioning what you do plan to do. It can confused the learner.
He DID a log.
Maybe you gave up before minute 11:30
3^x = 20
x(log3) = log20
x = (log20)/(log3)
x = 2.727 (rounded)
I think that the value of the ratio here [ (log20)/(log3)) ] will remain constant regardless the value that the bases have, assuming that the bases are the same. This allows the expression to be written as "log 20 base 3". .. (note that log a base a = 1).
To solve 3x=203^x = 20, you can use logarithms. Here's the step-by-step process:
Start with the equation:
3x=203^x = 20
Take the natural logarithm (ln\ln) on both sides:
ln(3x)=ln(20)\ln(3^x) = \ln(20)
Use the power rule of logarithms (ln(ab)=bln(a)\ln(a^b) = b \ln(a)):
xln(3)=ln(20)x \ln(3) = \ln(20)
Solve for xx:
x=ln(20)ln(3)x = \frac{\ln(20)}{\ln(3)}
Calculate the result using a calculator:
x≈2.99571.0986≈2.73x \approx \frac{2.9957}{1.0986} \approx 2.73
So, x≈2.73x \approx 2.73.
This approach works for exponential equations that don’t have integer solutions. Tools like SolutionInn's AI study aids can make equations like this easier to master by offering step-by-step explanations and plenty of practice problems tailored to your needs.
3×3×3 =27
3×3 =9
20 = 3^?2.5 = 15.59
3^2.6=17.40
3^2.7=19.42
3^2.71=19.63
3^2.74=20.29
3^2.73=20.07
x=2.73
I have to wonder why your video (and many similar videos on this type of problem) use the log rule that log 3^x = x log 3 when a much simpler procedure is to take log base 3 of 3^x and log base 3 of 20. Then you have x = log base 3 of 20 = ln 20/ln 3, which gives the same answer and is so much quicker. And it can be quickly computed on a calculator.
"Don´t know what a slide rule is for" Sam Cooke 1959 ❤
Works in any base of course as the ratios are the same.
I remember in High-School (1961-1964) there was a course called Confucian, a sort of high school advanced Algebra / Calculus course that had log tables at the end of the book. I even remember there was a complete book of log tables. I also, for some reason, bought a Picket Slide Rule and even had some vague idea of how to use it. I bought that sometime in the late 60s and still have it, complete with stiff leather holder.
In the end, I thought Math presented an awful lot of work for very small results. And Literature was far more practical.
I agree because we use grammar and linguistics on a daily basis compared to math
Thank you
Log_3(20) : x
Log_base (answer) : exponent
It is a one step solution.
I understood the method presented to solve for x by logs but I’m confused about x=2.72 in the first place.
So, 3^2 is 3*3, and 3^3 is 3*3*3. That’s seems clear because I see the exp. is the number of times the base value is multiplied by itself.
But 3^2.72 ? It’s not 3*3*(3*0.72) as this isn’t nearly equal to 20.
If x = 2.74, and 3^2.74 = 3*3*(3*0.74), that would be closer to 20. So I don’t get it fundamentally.
Using trial and error a number of times, you can get: 2.726833
But logs are easier because log(20) / log(3) = 2.726833
perfect!
For those wanting a bit of history, engineers and scientists used to do it the same way with a slide rule.
15:10 You're going to need Log Tables, a slide rule OR a calculator!
We had a demonstration slide rule hanging on the wall by the blackboard, about 5' long, that the professor used to teach our class how to use them. I wonder where all those went? A museum?
3^X = 20
LOG(3^x) = LOG(20)
X*LOG(3) = LOG(10) + LOG(2)
X = (1 + LOG(2))/LOG(3)
Therefore X equal approx. 2.727
0:48 2.726 rounds off to 2.73, not 2.72.
Space and time will not allow us to use numbers, nobody knows what 1 ( one ) is. We can only use matter on a grand scale.
2.7268 exactly!! :)
Nope, not exact, x is transcendental
No, not 2 times itself four times but 2 used as a factor four times is correct.
The word is NOT “prol-em”! It is “prob-lem.”
I got 2.726833 using ln20/ln3. My calculator lacks a log button. I still have a K&E Deci-Lon slide rule but I've forgotten how to use it!.
Keep your K&E from getting wet. It should outlive you.
How to with no calculator?
a little bit less than 3..,
🙋🤦🤷 and that was an instant thought lol...
When I took Trigonometry and Algebra II, I had to use a slide rule. I think I still have a slide rule. I heard it can be done on an abacus, but I don't know how.
In 1972 I competed in UIL drama and poetry interpretation (get the picture of my expertise?) My math teacher asked me to sign up for slide rule because the school got points for entrants regardless of how they did. I was actually a little proud of myself for coming in 11th out of 12 entrants because I didn't come in last.
Sir with all the respect ,You are a salesman not a math teacher ,Math teaches job is to make math easy .you complicated the issue .
xlog3 = log20 => x = (2log2)(log5)/log3
x=log3(20) > x= 2.72683
x≈2.73 (rounded)
3x = 20
x = log20/log3
x = 2.72683
3^2.72683 = 20
Wonderfully succinct and concise - so easlity assimilated in SECONDS, rather than 30 minutes 😕
Easily…..
I still have my Slide ruler's that I had back in High School in my Electronic class, Some Time known as a Slip Stick...
log20 / log3 = factor of 3 to result in 20.
x = log(base 3) of 20.
Well, what you do is use logarithms.
I had a circular slide rule
Very nice, but you lose the coolness of sticking it in your shirt pocket.
What about xlog 3 =log20
X=log20/log3
yeap i remember those tables also remember sliding rule
that is very difficult, i searched naver about power of a fraction.
all i got was a scientific calculator...i powered many times to get 2.726...
Yikes! Please just show us how to solve!
5x3=15 of that simble is the same thing
Xpower 20/3
As a teacher you have much to reconsider.
*leave much to be desired
X={1+log2}/log3........May be
So much messing around just apply a log10 base on both sides and this end up x=log20/log3
You mean back around 1935?
Ln20/Ln3 = 2.726833…
X ~~2.72…
3.14rootof
Could you come to the point? You are confusing people rather than solving the problem.
x = ln20 / ln3 ≈ 2.76…
Is it just a coincidence that the answer is almost e (Euler's number)? Or did you choose 3 and 20 deliberately because it's nearly e?
John was thinking of "Three and twenty black birds baked in a pie..." but he made another mistake: it's supposed to be 4 & 20 blackbirds!
7
3^x = 20 -> herschrijf het in logaritmische vorm log₃(20)
log₃(20) = x
Change of base : log₃(20) = log20/log3
Uaing log? X log 3 =log 20, x= log20/log3
Too much description. It can be summarised within 5 minutes
LOL I guessed 2.62 without doing any math
Have you tried horse racing?
60
To get the answer. Get the log and the lookup the log in a log table... Tbh logarithms are such an idiotic thing. A relic from the past to make calculations more efficient that really shouldn't be around anymore
Why is thus video way longer than it has to be? Get to the point please!
Some of us like an expanded view of math not just running through the problem.
Colossal, overly drawn out explanation. You could have done this in two minutes. I'm sure well intentioned, but boring and sleep inducing.
How difficult would it be to show this on an actual calculator? Does RUclips pay you by the time you waste from your poor viewers? You could have done 10 examples instead of running memory sad lane. Are you teaching math, or history? English you could not teach to save your life. Invest in a remedial class.
Boring
X=2,715