Answer
a.) $\log_8 \frac{1}{8} = -1$
b.) $\log_2 \frac{1}{8} = -3$
Work Step by Step
$Express$ $the$ $equation$ $in$ $logarithmic$ $form:$
a.) $8^{-1} = \frac{1}{8}$
b.) $2^{-3} = \frac{1}{8}$
Exponential form to logarithmic form: $b^c = a \rightarrow \log_b a = c$
a.) $8^{-1} = \frac{1}{8}$
Plug in 8 for b, -1 for c, and $\frac{1}{8}$ for a
$8^{-1} = \frac{1}{8} \rightarrow \log_8 \frac{1}{8} = -1$
b.) $2^{-3} = \frac{1}{8}$
Plug in 2 for b, -3 for c, and $\frac{1}{8}$ for a
$2^{-3} = \frac{1}{8} \rightarrow \log_2 \frac{1}{8} = -3$