Precalculus Examples

$\log_{b} (\frac{m n^{2}}{p^{3}})$

Step 1

Rewrite $\log_{b} (\frac{m n^{2}}{p^{3}})$ as $\log_{b} (m n^{2}) - \log_{b} (p^{3})$ .

$\log_{b} (m n^{2}) - \log_{b} (p^{3})$

Step 2

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

$\log_{b} (m n^{2}) - (3 \log_{b} (p))$

Step 3

Multiply $3$ by $- 1$ .

$\log_{b} (m n^{2}) - 3 \log_{b} (p)$

Step 4

Rewrite $\log_{b} (m n^{2})$ as $\log_{b} (m) + \log_{b} (n^{2})$ .

$\log_{b} (m) + \log_{b} (n^{2}) - 3 \log_{b} (p)$

Step 5

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

$\log_{b} (m) + 2 \log_{b} (n) - 3 \log_{b} (p)$