## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$-4$
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, $\log_{1/2} 16 = \boxed{-4}$