Answer
$x=\frac{2}{5}$
Work Step by Step
We are given that $32^{x}=4$. Both of these numbers are powers of 2, so we can rewrite the equation as $(2^{5})^{x}=2^{5x}=2^{2}$.
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $5x=2$.
Divide both sides by 5.
$x=\frac{2}{5}$
