Question

Change the following from logarithmic form to exponential form.
(i) ${\log }_{4}64=3$
(ii) ${\log }_{16}2=\frac{1}{4}$
(iii) ${\log }_5\left(\frac{1}{25}\right)=-2$
(iv) ${\log }_{10}0.1=-1$

Answer 1

(i) ${\log }_{4}64=3⟹4^3=64$
(ii) ${\log }_{16}2=\frac{1}{4}⟹{\left(16\right)}^{\frac{1}{4}}=2$
(iii) ${\log }_5\left(\frac{1}{25}\right)=-2⟹{\left(5\right)}^{-2}=\frac{1}{25}$
(iv) ${\log }_{10}0.1=-1⟹{\left(10\right)}^{-1}=0.1$