Question

Express the following in Exponential form :
(i) ${\log }_{9}6561=4$
(ii) ${\log }_{1/16}\left(\frac{1}{8}\right)=\frac{3}{4}$
(iii) ${\log }_{0.5}0.125=3$
(iv) ${\log }_2\frac{1}{4}=-2$

Answer 1

(1)

${\log }_{9}6561=4$

$\Rightarrow (9{)}^4=6561$ ( exponential form )

(2)

${\log }_{\frac{1}{16}}\left(\frac{1}{8}\right)=\frac{3}{4}$

$\Rightarrow {\left(\frac{1}{16}\right)}^{\frac{3}{4}}=\frac{1}{8}$ ( exponential form )