Answer
$-4$
Work Step by Step
Since $y=\log_a x \text{ is equivalent to } x= a^y$
Thus, if $y = \log_{1/2} 16$, then $\left(\dfrac{1}{2}\right)^y=16$.
Note that:
$16=2^4=\left(\dfrac{1}{2}\right)^{-4}$
Therefore,
$\left(\dfrac{1}{2}\right)^y=\left(\dfrac{1}{2}\right)^{-4}$
Use the rule $a^m=a^n \implies m=n$ to obtain:
$y=-4$
Hence,
$ \log_{1/2} 16 = \boxed{-4}$
