Answer
{$\frac{1}{64}$}
Work Step by Step
Using logarithmic principles, $\log_{4} x=-3$ can be changed to $x=4^{-3}$.
Solving further,
$x=4^{-3}=\frac{1}{4^{3}}=\frac{1}{64}$
Therefore, the solution set is {$\frac{1}{64}$}.
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