Answer
(a) $\log_{2}32= 5$
(b) $\log_{8}2= 0.3333$
Work Step by Step
(a) $\log_{2}32= \log_{2}(2^{5})$
Since, $logx^{y}=xlogy$
$\log_{2}32= \log_{2}(2^{5})$
Use logarithmic base formula $\log_{b}x=\frac{log x}{log b}$
$\log_{2}(2^{5}) =5\log_{2}2=5\times\frac{log 2}{log 2}$
Hence, $\log_{2}32= 5$
(b) Since, $\log_{b}x=\frac{log x}{log b}$
$\log_{8}2 =\frac{log 2}{log 8}$
Hence, $\log_{8}2= 0.3333$
