#### Answer

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

#### Work Step by Step

We are given the exponential equation $4^{x}=32$.
We can express each side using a common base and then solve for $x$.
$4^{x}=(2^{2})^{x}=2^{2x}$
$32=2^{5}$
$2^{2x}=2^{5}$
Take the natural log of both sides.
$ln(2^{2x})=ln(2^{5})$
$2xln(2)=5ln(2)$
Divide both sides by $ln(2)$.
$2x=5$
Divide both sides by 2.
$x=\frac{5}{2}$