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uranmaximum [27]
2 years ago
10

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

Mathematics
1 answer:
elena55 [62]2 years ago
8 0

Answer:

x=(243)log_{\frac{1}{81}}[(\frac{1}{81})-1]

Step-by-step explanation:

you have the following formula:

(\frac{1}{81})^{\frac{x}{243}}=(\frac{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_{(\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]

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