Question

question
evaluate:
$log_{81} \frac{1}{27}$
answer

Explanation:

Step1: Rewrite terms as powers of 3

$81 = 3^4$, $\frac{1}{27}=3^{-3}$

Step2: Apply logarithm base change rule

$\log_{3^4} 3^{-3} = \frac{\log_{3}3^{-3}}{\log_{3}3^4}$

Step3: Use log power rule $\log_a a^k=k$

$\frac{-3}{4}$

Answer:

$\frac{-3}{4}$