Answer
$y=\frac{1}{2} \cdot 2^x$
Work Step by Step
To find the inverse of the given function, perform the following steps:
(1) Interchange $x$ and $y$:
$$x=\log_2{2y}$$
(2) Write the equation in exponential form using the definition $y=\log_a{x} \longleftrightarrow a^y=x$:
$$2^x=2y$$
(3) Solve for $y$:
\begin{align*}
2^x&=2y\\\\
\frac{2^x}{2}&=y\\\\
y&=\frac{1}{2} \cdot 2^x
\end{align*}