Answer
$x=\frac{3}{2}$
Work Step by Step
We are given that $4^{x}=8$. Both of these numbers are powers of 2, so we can rewrite the equation as $(2^{2})^{x}=2^{2x}=2^{3}$.
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, $2x=3$.
Divide both sides by 2.
$x=\frac{3}{2}$
