Answer:
[tex]x=(243)log_{\frac{1}{81}}[(\frac{1}{81})-1][/tex]
Step-by-step explanation:
you have the following formula:
[tex](\frac{1}{81})^{\frac{x}{243}}=(\frac{1}{9})^{-3}-1[/tex]
To solve this equation you use the following properties:
[tex]log_aa^x=x[/tex]
Thne, by using this propwerty in the equation (1) you obtain for x
[tex]log_{(\frac{1}{81})}(\frac{1}{81})^{\frac{x}{243}}=log_{\frac{1}{81}}[(\frac{1}{81})-1]\\\\\frac{x}{243}=log_{\frac{1}{81}}[(\frac{1}{81})-1]\\\\x=(243)log_{\frac{1}{81}}[(\frac{1}{81})-1][/tex]
