Question

Express the following logarithms in terms of $\log a,\log b$, and $\log c$.
$\log \left(\sqrt[9]{9a^{-4}{b}^3}\right)$.

Answer 1

$\log \left(\sqrt[9]{9a^{-4}{b}^3}\right)=\log (a^{-4}{b}^3{)}^{\frac{1}{9}}=\frac{1}{9}\log a^{-4}{b}^3=\frac{1}{9}(-4\log a+3\log b)=-\frac{4}{9}\log a+\frac{1}{3}\log b$