Question

rewrite in log form: $8^{-3} = \frac{1}{512}$
$\log_{8}(-3) = \frac{1}{512}$
$\log_{8} \frac{1}{512} = -3$
$\log_{-3}8 = \frac{1}{512}$
$\log_{\frac{1}{512}}8 = -3$

Explanation:

Step1: Recall exponent-log conversion rule

For $b^y = x$, $\log_b x = y$

Step2: Match values to the rule

Here $b=8$, $y=-3$, $x=\frac{1}{512}$
Substitute into $\log_b x = y$: $\log_8 \frac{1}{512} = -3$

Answer:

B. $\log_8 \frac{1}{512} = -3$