Answer
$\log_2{\frac{1}{16}}=-4$
Work Step by Step
RECALL:
$b^y=x \longleftrightarrow \log_b{x} =y .$
Use the definition above to obtain
$2^{-4} = \frac{1}{16} \longrightarrow \log_2{\frac{1}{16}}=-4.$
Thus, the equivalent logarithmic form of the given expression is
$\log_2{\frac{1}{16}}=-4.$