Question

Solve the following :

$\log \frac{\sqrt[3]{3a{b}^{-1}{c}^{-2}}}{(a^{-1}{b}^{-2}{c}^{-4}{)}^{\frac{1}{6}}}$.

Answer 1

$\log \frac{\sqrt[3]{3a{b}^{-1}{c}^{-2}}}{{\left(a^{-1}{b}^{-2}{c}^{-4}\right)}^{\frac{1}{6}}}=\log \frac{a^{\frac{1}{3}}{b}^{\frac{-1}{3}}{c}^{\frac{-2}{3}}}{a^{\frac{-1}{6}}{b}^{\frac{-1}{3}}{c}^{\frac{-2}{3}}}=\log a^{\frac{1}{2}}=\frac{1}{2}\log a$