Answer
$x=\frac{1}{64}$
Work Step by Step
From the definition of the logarithmic function on page 456, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$, $b\gt0$, and $b\ne1$).
Therefore, $log_{4}x=-3$ is equivalent to $4^{-3}=x$ in logarithmic form.
We know that $4^{-3}=\frac{1}{4^{3}}=\frac{1}{64}$, so $x=\frac{1}{64}$.
