Answer
$x = \frac{1}{2}$
Work Step by Step
Let
$\log_{64}{8} = x$
RECALL:
$\log_b{y} =x \longrightarrow b^x=y$
Use the rule above, where $y=8$ and $b=64$, to obtain:
$64^x=8^{1}$
Write 64 as $8^2$ to obtain:
$(8^2)^x=8^{1}
\\8^{2x} = 8^{1}$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$2x=1
\\x = \frac{1}{2}$
