#### Answer

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

#### Work Step by Step

$32^{x}=4$
Rewrite $32$ as $2^{5}$ and $4$ as $2^{2}$
$(2^{5})^{x}=2^{2}$
Transform the left side of the equation into a power that has the product of $5$ and $x$ as its exponent:
$2^{5x}=2^{2}$
If $2^{5x}=2^{2}$, then $5x=2$:
$5x=2$
Solve for $x$:
$x=\dfrac{2}{5}$