Question

Express the following logarithms in terms of $\log a+\log b$, and $\log c$.
$\log (\sqrt[3]{3a^2}\times \sqrt[2]{2b^3})$.

Answer 1

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