#### Answer

$x=\dfrac{5}{2}$

#### Work Step by Step

Using the laws of exponents, the given equation, $
4^x=32
,$ is equivalent to
\begin{array}{l}\require{cancel}
(2^2)^x=2^5
\\\\
2^{2x}=2^5
.\end{array}
Since the bases are the same, the exponents can be equated. Hence,
\begin{array}{l}\require{cancel}
2x=5
\\\\
x=\dfrac{5}{2}
.\end{array}