#### Answer

$x=\frac{3}{4}$

#### Work Step by Step

We are given that $16^{x}=8$. Both of these numbers are powers of 2, so we can rewrite the equation as $(2^{4})^{x}=2^{4x}=2^{3}$.
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, $4x=3$.
Divide both sides by 4.
$x=\frac{3}{4}$