Expand the Logarithmic Expression log base b of (x^2y)/(z^8)

$\log_{b} (\frac{x^{2} y}{z^{8}})$

Step 1

Rewrite $\log_{b} (\frac{x^{2} y}{z^{8}})$ as $\log_{b} (x^{2} y) - \log_{b} (z^{8})$ .

$\log_{b} (x^{2} y) - \log_{b} (z^{8})$

Step 2

Expand $\log_{b} (z^{8})$ by moving $8$ outside the logarithm.

$\log_{b} (x^{2} y) - (8 \log_{b} (z))$

Step 3

Multiply $8$ by $- 1$ .

$\log_{b} (x^{2} y) - 8 \log_{b} (z)$

Step 4

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

$\log_{b} (x^{2}) + \log_{b} (y) - 8 \log_{b} (z)$

Step 5

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

$2 \log_{b} (x) + \log_{b} (y) - 8 \log_{b} (z)$