Question

Solve the following :

$\log (\sqrt[3]{3a^{-1}\sqrt{b^3}}÷\sqrt{b^3\sqrt{a}})$.

Answer 1

$\log (\sqrt[3]{3a^{-1}\sqrt{b^3}}÷\sqrt{b^3\sqrt{a}})=\log \left(a^{\frac{-1}{3}}{b}^{\frac{1}{2}}÷a^{\frac{1}{4}}{b}^{\frac{3}{2}}\right)=\log a^{\frac{-7}{12}}{b}^{-1}=-\frac{7}{12}\log a-\log b$