Solve for $x$ \[ \log _{x} \frac{1}{64}=-2 \]

Step 1 ：Solve for $x$ in the equation $\log _{x} \frac{1}{64}=-2$

Step 2 ：Rewrite the logarithmic equation in exponential form: $x^{-2} = \frac{1}{64}$

Step 3 ：Solve for $x$ to get the solutions $x = -8$ and $x = 8$

Step 4 ：However, in the context of logarithms, the base of a logarithm (x in this case) must be greater than 0 and not equal to 1. Therefore, $x = -8$ is not a valid solution

Step 5 ：Final Answer: The solution to the equation is $x = \boxed{8}$