Answer
$-3$
Work Step by Step
Recall the logarithmic property:
$\log_a a^x =x$
We wish to simplify $\log_2 (\dfrac{1}{8})$
We apply the property above to get:
$\log_2 (\dfrac{1}{8})=\log_2 (\dfrac{1}{2^3}) \\=\log_2 (2^{-3}) \\=-3$
Thus, $\log_2 (\dfrac{1}{8})=-3$