Answer
$1$
Work Step by Step
RECALL:
(i) $\log_b{b}=1$
(ii) $\log_b{b^x}=x$
(iii) $\log_b{1} = 0.$
Note that $32=2^5$. Thus, the given expression can be written as
$\log_5{(\log_2{2^5})}.$
Use rule (ii) above to obtain:
$\log_5{(\log_2{2^5})}=\log_5{5}.$
Use rule (i) above to obtain
$\log_5{5} = 1.$
