Answer
$\log _{b} 100=14$
Work Step by Step
Given log $_{b} 5=10$, $\log _{b} 20=4$
log $_{b} 100=?$
Using $\log _{b} m n=\log _{b} m+\log _{b} n$
Put m=5, n=20
$\therefore \log _{b}(5 \times 20)=\log _{b} 5+\log _{b} 20$
$\Rightarrow \log _{b} 100=10+4$
$\therefore \log _{b} 100=14$
