Answer
$\left\{32\right\}$
Work Step by Step
Since $\log_b y=x$ implies $b^x=y$, the given equation, $
\log_{1/2} x=-5
$, implies
\begin{align*}\require{cancel}
\left(\dfrac{1}{2}\right)^{-5}&=x
.\end{align*}
Using the laws of exponents, the equation above is equivalent to
\begin{align*}\require{cancel}
\dfrac{1}{\left(\frac{1}{2}\right)^{5}}&=x
\\\\
\dfrac{1}{\frac{1}{32}}&=x
\\\\
32&=x
.\end{align*}
Hence, the solution set of the equation $
\log_{1/2} x=-5
$ is $
\left\{32\right\}
$.
