Answer
$x=6$
Work Step by Step
First, we let
$\log_{2}{64} = x$
RECALL:
$\log_b{y} =x \longrightarrow b^x=y$
Use the rule above, where y=64 and b=2, to obtain:
$2^x=64$
Write 64 as $ 2^6$ to obtain:
$2^x=2^6$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$x=6$