Solve for x : 4^x + 6^x = 9^x

Solve for x : 4^x + 6^x = 9^x Thanks for watching.
Let me share with you how Numbers became
my FRIENDS in childhood.
I was in a strict residential hostel (Almost
like PRISON.) 3rd grade to 10th grade. The
students are not allowed to talk to each other
at most of the places. Also, you need to
close your eyes when you were told to sleep
irrespective of whether you are sleepy or not.
As I was alone, I started talking to numbers and
visualised playing with them.
By 6th class, I completed tables upto 100.
By 7th class, I was able to tell 3 digit by 3 digit
multiplications very fast..before calculator.
By 10th class, I was able to do 4 digit by 4 digit
multiplications without any shortcuts, just by
multiplying in brain.. I gave a show as a fresher in GITAM
engineering college in1988 where anyone can
ask
Squares, square roots, cubes, cube roots, 3x3
multiplications. My timing was checked with
calculator..and I was quicker than calculator.
My nick name in college was HUMAN
CALCULATOR. (I know l am not even 0.001%
eligible to be called as one :))
That's how numbers became part of my daily
life.
So, you leave me in a place where no one
present,I can still manage without TV or
mobile.
My friends (Numbers) are always there to give
company. :)

[Aditya-kusb]

Very good video, and your story is absolutely amazing as well. You're an inspiration sir. Keep changing lives :)

[diptumint]

Very well done. I appreciate that you have solved it fully on one screen, by using different colors. Thank you.

[munfac.b]

Hay ....solv 》》 1^x + 6^x + 8^x = 9^x The answer is 3, but I relied on experience... and I did not find a way to solve it mathematically

[nickubossvainglory]

Alternatively, you can do this approach:
4^x + 6^x = 9^x
=> 4^x (1^2) + 6^x (1) -9^x = 0
So, using the quadratic formula,
1 = -6^x +_ sqrt(6^2x+4*4^x*9^x)/...
=-6^x +_ sqrt(6^2x+4*6^2x)/...
=-6^x +_ sqrt(5)*6^x/...
= (-6^x(1+_sqrr(5)))/2*4^x
As 1 > 0, and a^x > 0 if a > 0
We replace +_ with - to make RHS positive.
=> 1 = (6/4)^x*(sqrt(5)-1)/2
=> x = log(2/(sqrt(5)-1))/log(6/4) = 1.1868...

[Albert-cttt]

Sorry, yr. method is too long and cumbersome. I found another shorter way. As 4^1 + 6^1 = 10, namely a bit larger than 9^1 = 9, and 4^1.1 + 6^1.1 = 4.6 + 7.1 = 11.7, namely larger than 9^1.1 ( which is 11.2), whereas 4^1.2 + 6^1.2 = 5.27 + 8.58 = 13.85, namely smaller than 9^1.2 (which is 13.96), thus x is bound to be found between 1.1 and 1.2 (and very close to 1.2). And finally, if you try x = 1.19, then you immediately find this is the correct value. It took me only 4 steps to prove it.

[atzerreo]

I had a lot of trouble with this one until I realised that 4*3/2=6 and that 4*(3/2)²=9.
once you've noticed it it's really easy.

[pythagorasaurusrex]

The solution is faster when you divide the equation by 4^x in the first place and bring the right side to the left.
You immediately get: (9/4)^x-(3/2)^x-1=0. As 9/4 is just (3/2)^2, you can substitute (3/2)^x=u and get u^2-u-1=0. The rest follows as usual

[rajvardhanpowar]

Thank you so much sir 🙏 . You are can very helpful ☺️ teacher keep helping others ☺️ . While helping others happiness is there . Nice 👍 Explanation ☺️. Thank you sir ☺️ .

[Zyerix]

how did you get 1.1868 from that? did you use a calculator or did you calculate it yourself?

[smlt]

Can we prove that 6+4=9 ?
Is it possible in maths?

[piotrsobodzian]

The closed form solution is: x = asinh(-0.5)/ln(2/3) and x = -asinh(-0.5)/ln(2/3)

[rohitdalai]

Thank you so much for such easy explaination

[nebthegamerartist]

Surprised you use logs compared to ln natural log, I find ln easier to understand since I got my head around “e” but i guess this works!

[kajalkumari-jonu]

Too easy for understanding thanku so much for taught us....🙏🙏

[jawowlo]

Is there any way to solve without using logarithms?

[pinkysahni]

How to become z value? I am not understand.🤔

[swatibarnawal]

√4-x+√x+9=5
Sir how to do this problem ?

[ppadma]

You are great sir will you take tutions

[newstime]

Pls help, Why did u write(2^2)^x as (2^x)^2 I did not understand how this can be written

[sadeghdanaei]

You calculated the equation wrong. And then put the right answer from somewhere.
Simply look at the denominator you showed: (log2- log3 ) it is a minus value. Simple common that you didn't care .
Even though the numerator you found is wrong too.
The right answer is : (log( 1+√ 5) - log2 ) /( log 3 - log2 )