Question

Express the logarithm of $\frac{\sqrt{a^3}}{c^5{b}^2}$ in terms of $\log a,\log b$ and $\log c$.

Answer 1

$\log \frac{\sqrt{a^3}}{c^5{b}^2}=\log \frac{a^{\frac{3}{2}}}{c^5{b}^2}$
$=\log a^{\frac{3}{2}}-\log \left(c^5{b}^2\right)$
$=\frac{3}{2}\log a-(\log c^5+\log b^2)$
$=\frac{3}{2}\log a-5\log c-2\log b$.