Expand the Logarithmic Expression log base b of (x^3y)/(z^9)

$\log_{b} (\frac{x^{3} y}{z^{9}})$

Rewrite $\log_{b} (\frac{x^{3} y}{z^{9}})$ as $\log_{b} (x^{3} y) - \log_{b} (z^{9})$ .

$\log_{b} (x^{3} y) - \log_{b} (z^{9})$

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

$\log_{b} (x^{3} y) - (9 \log_{b} (z))$

Multiply $9$ by $- 1$ .

$\log_{b} (x^{3} y) - 9 \log_{b} (z)$

Rewrite $\log_{b} (x^{3} y)$ as $\log_{b} (x^{3}) + \log_{b} (y)$ .

$\log_{b} (x^{3}) + \log_{b} (y) - 9 \log_{b} (z)$

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

$3 \log_{b} (x) + \log_{b} (y) - 9 \log_{b} (z)$