Answer
{$8$}
Work Step by Step
Step 1: $\log_{x} 64=2$
Step 2: $x^{2}=64$
Step 3: $\sqrt {x^{2}}=\pm\sqrt {64}$
Step 4: $x=+8$, as -8 is discarded since the base of a logarithm cannot be negative.
Therefore, the solution set is {$8$}.
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