Question

Solve the following :

$\log (\sqrt{a^{-2}b}\times \sqrt[3]{3a{b}^{-3}})$.

Answer 1

$\log (\sqrt{a^{-2}b}\times \sqrt[3]{3a{b}^{-3}})=\log a^{-1}{b}^{\frac{1}{2}}\times a^{\frac{1}{3}}{b}^{-1}=\log a^{\frac{-2}{3}}{b}^{\frac{-1}{2}}=-\frac{2}{3}\log a-\frac{1}{2}\log b$