Question

Write $3^{-4}=\frac{1}{81}$ in logarithmic form.

Answer 1

$3^{-4}=\frac{1}{81}$

Applying $\log$ both sides, we get

${\log }_3{3}^{-4}={\log }_3\left(\frac{1}{81}\right)$

$\Rightarrow -4{\log }_{3}3={\log }_3\left(\frac{1}{81}\right)$

using $\log a^m=m\log a$

$\Rightarrow -4={\log }_3\left(\frac{1}{81}\right)$ using ${\log }_{a}a=1$

$\therefore {\log }_3\left(\frac{1}{81}\right)=-4$