Question

Prove that $\log \frac{75}{16}-2\log \frac{5}{9}+\log \frac{32}{243}=\log 2$.

Answer 1

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

Hence proved