Answer
$ \log _{b} 32=7$
Work Step by Step
Given
\[
\begin{array}{l}
\log _{b} 2=3 \quad, \log _{b} 16=4 \\
\log _{b} 32=?
\end{array}
\]
Using
\[
\log _{b} m n=\log _{b} m+\log _{b} n
\]
Put
\[
m=2, \quad n=16
\]
$\therefore \log _{b}(2 \times 16)=\log _{b} 2+\log _{b} 16$
\[
\begin{array}{l}
\Rightarrow \log _{b} 32=3+4 \\
\therefore \log _{b} 32=7
\end{array}
\]
