Answer
$2$
Work Step by Step
RECALL:
(i) $\log_b{b}=1.$
(ii) $\log_b{b^x}=x.$
(iii) $\log_b{1} = 0.$
Note that $81=3^4$. Thus, the given expression can be written as
$\log_2{(\log_3{3^4})}.$
Use rule (ii) above to obtain
$\log_2{(\log_3{3^4})}=\log_2{4} = \log_2{2^2}.$
Use rule (ii) above to obtain
$\log_2{2^2} =2.$
