SOLUTION: 4^(1-x)=3^(2x-5)

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Question 922509: 4^(1-x)=3^(2x-5)
Answer by Edwin McCravy(20060) 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