Why the answer is A, and why the others tempt you.
$\log_x 64 = 3$ means $x^3 = 64$, so $x = \sqrt[3]{64} = 4$. Candidates who confuse the base and the argument may choose 8 (since $8^2 = 64$) or 2 (since $2^6 = 64$).
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