Question

Express in terms of $\log m,\log n,\log p$ the expression $\log \frac{\left(m\sqrt[4]{4n}\right)}{\sqrt[3]{3p^5}}$

Answer 1

$\log \frac{\left(m\sqrt[4]{4n}\right)}{\sqrt[3]{3p^5}}$

$=\log \left(m\sqrt[4]{4n}\right)-\log \sqrt[3]{3p^5}$

$=\log m+\log n^{\frac{1}{4}}-\log (p{)}^{\frac{3}{5}}$

$=\log m+\frac{1}{4}\log n-\frac{3}{5}\log p$.