Answer
$ \log _{b} 15=-6
$
Not possible, log values Cannot be negative
Work Step by Step
\[
\begin{array}{c}
\text { Given } \log _{b} 30=8, \log _{b} 2=14 \\
\log _{b} 15=?
\end{array}
\]
Using $\log _{b}\left(\frac{m}{n}\right)=\log _{b} m-\log _{b} n$
\[
P u t \quad m=30, \quad n=2
\]
\[
\begin{array}{l}
\therefore \log _{b}\left(\frac{30}{2}\right)=\log _{b} 30-\log _{b} 2 \\
\Rightarrow \log _{b} 15=8-14 \\
\therefore \log _{b} 15=-6
\end{array}
\]
Not possible, log values Cannot be negative