Question

Solve (1/81)^x*1/243=(1/9)^−3−1 by rewriting each side with a common base.

Answer 1

`x=(243)log_{(1)/(81)}[((1)/(81))-1]`

Explanation:

you have the following formula:

`((1)/(81))^{(x)/(243)}=((1)/(9))^(-3)-1`

To solve this equation you use the following properties:

`log_aa^x=x`

Thne, by using this propwerty in the equation (1) you obtain for x

`log_{((1)/(81))}((1)/(81))^{(x)/(243)}=log_{(1)/(81)}[((1)/(81))-1]\\\\(x)/(243)=log_{(1)/(81)}[((1)/(81))-1]\\\\x=(243)log_{(1)/(81)}[((1)/(81))-1]`