Question

Express in term of $\log 2$ and $\log 3$:
$\log \frac{75}{16}-2\log \frac{5}{9}+\log \frac{32}{243}$

Answer 1

$\log \frac{75}{16}-2\log \frac{5}{9}+\log \frac{32}{243}$
$=\log \frac{75}{16}-\log \frac{25}{81}+\log \frac{32}{243}$
$=\log (\frac{75}{16}\cdot \frac{81}{25}\cdot \frac{32}{243})$
$=\log (\frac{3\cdot 25}{16}\cdot \frac{81}{25}\cdot \frac{2\cdot 16}{3\cdot 81})$
$=\log \left(2\right)$