Answer
$x=1$
Work Step by Step
Note that $64=4^3$, so the given equation is equivalent to:
$4^{3x}=4^3$
Using the rule $a^m=a^n\longrightarrow m=n$ gives:
$3x=3$
$x=\frac{3}{3}$
$x=1$
Check:
$4^{3*1}=64$
$4^{3}=64$
Thus, we have confirmed that the answer is correct.