Precalculus Examples

$\log_{5} (\frac{m^{2}}{\sqrt[3]{n}})$

Step 1

Rewrite $\log_{5} (\frac{m^{2}}{\sqrt[3]{n}})$ as $\log_{5} (m^{2}) - \log_{5} (\sqrt[3]{n})$ .

$\log_{5} (m^{2}) - \log_{5} (\sqrt[3]{n})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{n}$ as $n^{\frac{1}{3}}$ .

$\log_{5} (m^{2}) - \log_{5} (n^{\frac{1}{3}})$

Step 3

Expand $\log_{5} (m^{2})$ by moving $2$ outside the logarithm.

$2 \log_{5} (m) - \log_{5} (n^{\frac{1}{3}})$

Step 4

Expand $\log_{5} (n^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$2 \log_{5} (m) - (\frac{1}{3} \log_{5} (n))$

Step 5

Combine $\frac{1}{3}$ and $\log_{5} (n)$ .

$2 \log_{5} (m) - \frac{\log_{5} (n)}{3}$