2 to the x = 12, many don’t know where to start
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- Опубликовано: 3 июл 2024
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You have no idea how much you help me with math. Im fourteen and learning math everyday because of you. Thank you 😊
How sweet and humble you are to appreciate Mr John’s hard work!
(I needed to add more to this message)
You are only 14 years old!
I am 73 and I should be old enough to be your grandmother.
I may share some wisdom gained over the years.
Humbleness is a worthwhile wholesome quality to have.
I think all babies are born with humility, but they tend to lose it as they grow up, because they get influenced by the corrupted society around them.
So, please try not to lose your humbleness as you go through life.
Life is much more than learning Mathematics. However, when you focus your mind on Mathematics, it helps your mind to keep away from trouble! 😇
I think, overall, this math channel gives us opportunities to observe how we all behave when we can’t do a math problem correctly.
Some people’s ego gets hurt and they blame others!
So, we get a chance to notice those shortcomings in the real world, learn how to remain humble with compassion and become better humans!
If those videos ONLY help you, he have achieved his goal.
@@chrisdissanayake6979 Thank you❤️
@@Kualinar yes he has☺️
@@shanoxyshanoxy1230🙏🏽♥️
Good Class! Thanks, I had forgotten this since 1963.
Great class!
The property of logarithms one needs to know for solving these problems is the log of a number to an exponent is the same as the exponent times the log of the number. This is a good practice problem for this property.
This lesson was a LOT more complex than the problem looked.
X = log(12)/log(2) = 3.58496...
Better approach
Thank you
3.5849625 X = log(12) / log(2) used calculator for the logs. Did this before watching the video. Logarithms are a frequent "go to" if unknown is in the exponent.
But how does a person manually calculate the log function of a calculator? Trial and error?
got it kinda solved mentally logic gave me 3.6 good explanation thanks for the fun
1) 2^x=12 ==> xln2 = ln12 ==> x= ln12/ln2.
2) 2^(ln12/ln2)=12.
8 seconds to calculate, not 1150 seconds (19 mn 10)
OR 2^x = 2^3.584. Both sides have a common base i.e 2 so x = 3.584
this is a question about ASU vs meteric when is 32'=to 9 meters?? gravity acieration or is the meteric number wrong and should be 9.81meters per sec per sec
6 maybe unsure, thank you I learned something new.
I never remember how to do this, but it’s easy to derive on the fly. Another way to express the value 2 is 10^log(2).
12 is then 10^log(2)^x, or 10^(log(2)*x). In other words, the base ten log of 12 is log(2)*x. The base 2 log is log(12)/log(2), which gives you the answer.
I would love to see a video explaining your rounding technique😉
Kinda like the brutal butchering, but......
That stretched my 64 Yr old brain! Thanks for the exercise 👍
😊😊😊😊 casi 20 minutos para darte vueltas, como un verdadero mojón en el agua, pensé que iba ver algo extraordinario 😢
A log is the inverse of an exponential,
2 to 3.5
I used logic to solve this problem meaning that we are actually solving for the sq root of 12 so the exponent needs to be the sq root of 12 which is 3.46410161513775. Plug that into the x value and you get 12.
This seems to work only when dealing with base 2 so the log solution is the better way to go.
2^(✓12)= 11.035665... That's smaller than 12.
2^(ln12/ln2) = 12. 2^(log12/log2) = 12. ln12/ln2 = 3.2849625... log12/log2 = 3.2849625...
The only way to get the correct answer is to use logarithm, not a square root.
Log 6 with base 2. Eg: Log₂ 6 = x
Is just the definition of log2(12).
X=log12 à la base 2
I taught this to primary kids I.e, 11 year olds . You just start with base 2 and make a table of answers
Eg Base Exponent Answer
2 0 1
2 1 2
2 2 4
2 3 8
2 4 16
2 5 32
Obviously expanded further. You then compare the exponents to the answers . The log is the index or
Exponent to that base.
So log 16 in base 2 is 4 . Just look at the table. A kid can see this.
When you see equations with x as a power think logs.
3.58496
Log-e 12/Log-e 2
2^x = 12
x log 2 = log 12
x = log 12/ log 2
x = 3,5849
log(2^X)=log(12)
X×log(2)=log(4)+log(3)
X=(log(4)+log(3))/log(2)
X=log(4)/log(2)+log(3)/log(2)
X=2+log(3)/log(2)
I'm surprised it wasn't a linear power (3.5).
x = 2 + ln(3) / ln(2) OR ln(12)/ln(2)
The natural logarithm of 12 divided by the natural logarithm of 2 equals 2 plus the natural logarithm of 3 divided by the natural logarithm of 2.
5
To involved lets similfy the explanation.KISS principle
Next, do fractional tetration.
THIS IS A GREAT VIDEO TO PLAY MULTIPLE TIMES TO ASSURE YOU GET EVERYTHING PRESENTED...
A L S O you MUST hardcore memorize about logs, exponents and bases....
This is possibly NEW notation.... so spend 10 minutes and commit it to memory. Repeat this lesson tomorrow.... Then search out other RUclipss on logarithms.
2^2 + 2^3 = 12
I.E.
4 + 8 = 12✔️
2^2+2^3 = 2^2(1+2)
= 2^2(3)
So
2^x = 2^2(3)
Xlog2= log(2^2(3))
X= log((2^2)(3))/log(2)
= ((2log2)+log(3)/(log2)
= (2(0.301)+(0.477))/(0.301)
= (2 + (0.477/0.301))
= (2+ 1.585)
= 3.585
Alternate
Xlog2=log12
X= log12/log2
= 3.585
My calculator came up with a similar solution, too, using natural logarithms.
That answer is ln(3) / ln(2) +2.
It also gave a solution called "root of the equation" with the solution using not base 10 log, but base 2 (aiming from value x?)
That answer was x = log2(3) + 2
Fantastic! That's what I got.
If "we're gonna type this into our calculator ",
why wouldn't we just type into our calculator
log12/log2?
Still remembered: ln(12)/ln(2)
2 to the x = 12, many don’t know where to start: 2³ = 8, 2ˣ = 12; x = ?
Straight forward solution:
log(2ˣ) = log12, x = log₂12 = log₂[(2²)(3)] = log₂(2²) + log₂3 = 2 + 1.585 = 3.585
Answer check:
2ˣ = 2³·⁵⁸⁵ = 12; Confirmed
The calculation was achieved on a smartphone with a standard calculator app
Final answer:
x = log₂12 = 3.585
2^(ln12/ln2)=12 , -> x=ln12/ln2 ,
Summing the 2 equations term to term, it follows :
2^2 +2^3=12
2^2*(1+2)=12
2^2*3=12
2^2*2^(log2(3))=12
2^(1+log2(3))=12
x=1+log2(3)
x=1+log(3)/log(2)
@@abdelwahabazeddine7035 checking your calculation , 2^(1+log(3)/log(2))=6 ??? , and not 12 ? not clear...
@prollysine
Exact. The error is obvious ( line 5) !!!
2^(2+log(3)/log(2))=12
x=2+log(3)/log(2)
Writing math equation in text mode is not easy.
Log2(3) means log(3) in base 2.
@@abdelwahabazeddine7035 First you wrote: x=1+log(3)/log(2) and now you write x=2+log(3)/log(2), the latter is correct, so x=2+log(3) /log(2) is the good result, have a nice day
@@prollysine
Of course the latter is the correct answer !!!
The direct method :
x=log(12)/log(2)
x=log(4*3)/log(2)
x=(log(4)+log(3))/log(2)
x=(log(2^2)+log(3))/log(2)
x=(2*log(2)+log(3))/log(2)
x=2+log(3)/log(2)
Six lines instead of five in previous method.
2 to the 4th
Its actually closer to 3.585.
x=log12/log2
This is the answer: 3.5849625007211561814537389439478
LOL
That is an approximation of the answer.
X=log 12/log 2
x is aprox 3.58
I am sorry I didn’t have a calculator.
I tried to do x log 2 = 12
So, it should be
Log 2 12 = x
Your computer or smart phone probably has a calculator.
@@richardl6751
Thank you 🙏🏽
But, I did it wrong.
x log 2 = log 12😊
@@barrychoi606
Thank You 🙏🏽
Its more than easy 12/ln2
xlog2=log12
x=log12/log2
x=log6
Log 12/ log2= log12 base2
The last time I did this in the lab where I worked, I was fired, so I learned logarithms. What a waste of time
7
If I didn't want to understand logarithms, I'd watch this video.
Easy. X= log 12 ÷ log 2 ≈ 3.585 (3.5849625....)
You can also use ln(12) ÷ ln 2 ≈ 3.585
Liking and posting a comment also help getting a video proposed to more peoples.
X=log12 ÷log2
X=3.5
So what I'm hearing is, if you don't have the proper calculator, there is little hope for this old man to figure this out? How did they do it before calculators?
X=log12/log2～=3.584962500721156
log(12) / log(2) = 3,5849625007211561814537389439
no idea here....42 yrs old
So basically just use a calculator. :)
Too long for explanation. Waste time.
Is this a joke?
This guy rabbits on and on . Introducing logs to the base e Euler’snumber then dividing by log base 2 with no explanation. The whole thing is a garbled mess. Sorry but he is crap at teaching and anyone who claims to have learnt anything aleady knew more advanced stuff.. What level he is teaching to is not defined. As a maths teacher I am at a loss to know how any of his children learnt from such a convoluted and mixed up message. Teaching is about simplifying not mixing up ideas . You start with the notion of a log as the inverse of an exponential. Establish this with examples then relate it to the problem. You do not try to tell people about other things like logs to base e. His other point was to establish why he was dividing by log base 2 with examples. Instead he just waffles on congratulating himself as if the object is proving how clever he is solving a very basic problem. Sorry but I despair!
Your teaching method is very poor
Useless. If you are going to rely on your calculator, why bother with the manual stuff?
It is the method to solve exponential equations, which could then reference logarithmic tables or a calculator to get a decimal number.
So that you understand what you are doing.
I guesstimated using the calculator and found it to be ALMOST 2^3.58499 which my calculator gave me the answer of 12.0002287347, so I figured it was close enough. ... I'm not weighing atoms here. (^_^)