Expand the Logarithmic Expression log base 9 of (4^3)/5

$\log_{9} (\frac{4^{3}}{5})$

Rewrite $\log_{9} (\frac{4^{3}}{5})$ as $\log_{9} (4^{3}) - \log_{9} (5)$ .

$\log_{9} (4^{3}) - \log_{9} (5)$

Expand $\log_{9} (4^{3})$ by moving $3$ outside the logarithm.

$3 \log_{9} (4) - \log_{9} (5)$

Rewrite $\log_{9} (4)$ as $\log_{9} (2^{2})$ .

$3 \log_{9} (2^{2}) - \log_{9} (5)$

Expand $\log_{9} (2^{2})$ by moving $2$ outside the logarithm.

$3 (2 \log_{9} (2)) - \log_{9} (5)$

Multiply $2$ by $3$ .

$6 \log_{9} (2) - \log_{9} (5)$