Answer
$200$
Work Step by Step
RECALL:
(1) $(a^m)^n=a^{mn}$
(2) $\log_b{(b^x)}=x$
Write $16$ as $4^2$ to obtain:
$=\log_4{[(4^2)^{100}]}$
Use rule (1) above to obtain:
$=\log_4{\left(4^{2(100)}\right)}
\\=\log_4{(4^{200})}$
Use rule (2) above to obtain:
$=200$
