c=(a^x−b^x) where a,b and c are known real constants. Solve for x.

Tiffany Page

Tiffany Page

Answered question

2022-11-04

c = ( a x b x ) where a, b and c are known real constants. Solve for x
I tried taking log on both side but i ended with log ( a x b x ) which is difficult to solve. Does anybody has idea how to solve the above equation for x

Answer & Explanation

Leo Robinson

Leo Robinson

Beginner2022-11-05Added 14 answers

I could try to simplify it a little:
c = a x b x = a x a x log a ( b )
a x = u
c = u u log a ( b )
0 = u log a ( b ) u + c
From here, you might notice that we can't solve for u because we can't solve the following general problem:
0 = x n + a x + c
If we could solve the above problem for any n, then we'd probably have things like algebraic solutions to quintic polynomials and such.
In fact, we pretty much can only solve this if:
0 n 4
And if n is an integer.
We see that log b ( a ) will most likely not be an integer and it will most likely not be between 4 , 0

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