Expand the Logarithmic Expression log base b of (x^3y)/(z^5)

$\log_{b} (\frac{x^{3} y}{z^{5}})$

Step 1

Rewrite $\log_{b} (\frac{x^{3} y}{z^{5}})$ as $\log_{b} (x^{3} y) - \log_{b} (z^{5})$ .

$\log_{b} (x^{3} y) - \log_{b} (z^{5})$

Step 2

Expand $\log_{b} (z^{5})$ by moving $5$ outside the logarithm.

$\log_{b} (x^{3} y) - (5 \log_{b} (z))$

Step 3

Multiply $5$ by $- 1$ .

$\log_{b} (x^{3} y) - 5 \log_{b} (z)$

Step 4

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

$\log_{b} (x^{3}) + \log_{b} (y) - 5 \log_{b} (z)$

Step 5

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

$3 \log_{b} (x) + \log_{b} (y) - 5 \log_{b} (z)$