SOLUTION: I need step-by-step to solve this equation: 4^(1-x)=3^(2x-5)

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Question 922516: I need step-by-step to solve this equation:
4^(1-x)=3^(2x-5)
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4^(1-x)=3^2x-5
-----------
(1-x)*log(4) = (2x-5)*log(3)
Can you do the rest?

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%281-x%29=3%5E%282x-5%29
We take the log of both sides:
log%284%5E%281-x%29%29=log%283%5E%282x-5%29%29
There is a rule of logarithms that allows us to move an exponent
in front as a multiplier of the log:
%281-x%29log%284%29=%282x-5%29log%283%29
To make things easier let log(4)=A and log(3)=B
%281-x%29A=%282x-5%29B
A%281-x%29=B%282x-5%29
A-Ax=2Bx-5B
A%2B5B=2Bx%2BAx
A%2B5B=%282B%2BA%29x
Divide both sides of the equation by (2B+A)
%28A%2B5B%29%2F%282B%2BA%29=x
Now replace A and B by the logs they represent:
%28log%284%29%2B5%2Alog%283%29%29%2F%282%2Alog%283%29%2Blog4%29=x
With a calculator we get
1.919720789 = x
Edwin