Expand the Logarithmic Expression log base b of (x^2y)/(z^2)

$\log_{b} (\frac{x^{2} y}{z^{2}})$

Rewrite $\log_{b} (\frac{x^{2} y}{z^{2}})$ as $\log_{b} (x^{2} y) - \log_{b} (z^{2})$ .

$\log_{b} (x^{2} y) - \log_{b} (z^{2})$

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

$\log_{b} (x^{2} y) - (2 \log_{b} (z))$

Multiply $2$ by $- 1$ .

$\log_{b} (x^{2} y) - 2 \log_{b} (z)$

Rewrite $\log_{b} (x^{2} y)$ as $\log_{b} (x^{2}) + \log_{b} (y)$ .

$\log_{b} (x^{2}) + \log_{b} (y) - 2 \log_{b} (z)$

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

$2 \log_{b} (x) + \log_{b} (y) - 2 \log_{b} (z)$