Answer
$2$
Work Step by Step
RECALL:
(i) $\log_b{b} = 1$
(ii) $\log_b{1}=0$
(iii) $\log_b{b^x} = x$
Write $81$ as $3^4$ to obtain:
$=\log_2{(\log_3{3^4})}$
With $b=3$ and $x=4$, use rule (iii) to obtain:
$\log_2{(\log_3{3^4})}=\log_2{4}$
Write $4$ as $2^2$ to obtain:
$=\log_2{2^2}$
Use rule (iii) above to obtain:
$\log_2{2^2}=2$
