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!❤👍
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.
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).
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.
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 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 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 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.
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.
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?
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
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.
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).
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
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 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
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.
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.
3x = 20
x = log20/log3
x = 2.72683
3^2.72683 = 20
"Don´t know what a slide rule is for" Sam Cooke 1959 ❤
No, not 2 times itself four times but 2 used as a factor four times is correct.
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
Works in any base of course as the ratios are the same.
0:48 2.726 rounds off to 2.73, not 2.72.
x=log3(20) > x= 2.72683
How to with no calculator?
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.
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?
x = log(base 3) of 20.
x≈2.73 (rounded)
What about xlog 3 =log20
X=log20/log3
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.
2.7268 exactly!! :)
Nope, not exact, x is transcendental
I had a circular slide rule
Very nice, but you lose the coolness of sticking it in your shirt pocket.
Thank you
log20 / log3 = factor of 3 to result in 20.
xlog3 = log20 => x = (2log2)(log5)/log3
X={1+log2}/log3........May be
5x3=15 of that simble is the same thing
3^x = 20 -> herschrijf het in logaritmische vorm log₃(20)
log₃(20) = x
Change of base : log₃(20) = log20/log3
Ln20/Ln3 = 2.726833…
X ~~2.72…
Uaing log? X log 3 =log 20, x= log20/log3
As a teacher you have much to reconsider.
*leave much to be desired
x = ln20 / ln3 ≈ 2.76…
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...
So much messing around just apply a log10 base on both sides and this end up x=log20/log3
3.14rootof
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!
yeap i remember those tables also remember sliding rule
a little bit less than 3..,
🙋🤦🤷 and that was an instant thought lol...
7
Too much description. It can be summarised within 5 minutes
60
LOL I guessed 2.62 without doing any math
Have you tried horse racing?
Yikes! Please just show us how to solve!
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
Could you come to the point? You are confusing people rather than solving 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.
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...
X=2,715