Expand the Logarithmic Expression log base b of (x^3y)/(z^2)

$\log_{b} (\frac{x^{3} y}{z^{2}})$

Step 1

Rewrite $\log_{b} (\frac{x^{3} y}{z^{2}})$ as $\log_{b} (x^{3} y) - \log_{b} (z^{2})$ .

$\log_{b} (x^{3} y) - \log_{b} (z^{2})$

Step 2

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

$\log_{b} (x^{3} y) - (2 \log_{b} (z))$

Step 3

Multiply $2$ by $- 1$ .

$\log_{b} (x^{3} y) - 2 \log_{b} (z)$

Step 4

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

$\log_{b} (x^{3}) + \log_{b} (y) - 2 \log_{b} (z)$

Step 5

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

$3 \log_{b} (x) + \log_{b} (y) - 2 \log_{b} (z)$