Answer
$x=2$
Work Step by Step
Note that $64=4^3$.
Write $64$ as $4^3$ to obtain:
$4^{2x-1}=4^3$
RECALL:
If $a^x = a^y$, then $x=y$.
Use the rule above to obtain:
$4^{2x-1}=4^3
\\2x-1=3
\\2x=3+1
\\2x=4
\\x=\frac{4}{2}
\\x=2$