Precalculus Examples

$\log_{b} (\frac{x y^{4}}{z^{6}})$

Rewrite $\log_{b} (\frac{x y^{4}}{z^{6}})$ as $\log_{b} (x y^{4}) - \log_{b} (z^{6})$ .

$\log_{b} (x y^{4}) - \log_{b} (z^{6})$

Expand $\log_{b} (z^{6})$ by moving $6$ outside the logarithm.

$\log_{b} (x y^{4}) - (6 \log_{b} (z))$

Multiply $6$ by $- 1$ .

$\log_{b} (x y^{4}) - 6 \log_{b} (z)$

Rewrite $\log_{b} (x y^{4})$ as $\log_{b} (x) + \log_{b} (y^{4})$ .

$\log_{b} (x) + \log_{b} (y^{4}) - 6 \log_{b} (z)$

Expand $\log_{b} (y^{4})$ by moving $4$ outside the logarithm.

$\log_{b} (x) + 4 \log_{b} (y) - 6 \log_{b} (z)$