Answer
$x=-3$
Work Step by Step
For $x\gt 0$ and $a$ a positive constant other than 1,
$\log_{a}x$ is the exponent to which $a$ must be raised in order to get $x$.
Thus, $\log_{a}x=m$ means $a^{m}=x$
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By definition, $\displaystyle \log_{1/4}\frac{1}{64}=x$ means
$x$ is the exponent with which we raise (1/4) to obtain 64
$4^{3}=64$
$(4^{-1})^{-3}=64$
$(\displaystyle \frac{1}{4})^{-3}=64$
so, $x=-3$