Answer
$99$
Work Step by Step
RECALL:
(1) $(a^m)^n=a^{mn}$
(2) $\log_b{(b^x)}=x$
Write $8$ as $2^3$ to obtain:
$=\log_2{[(2^3)^{33}]}$
Use rule (1) above to obtain:
$=\log_2{\left(2^{3(33)}\right)}
\\=\log_2{(2^{99})}$
Use rule (2) above to obtain:
$=99$