Precalculus Examples

$\log_{6} (c^{5} \sqrt[3]{a})$

Step 1

Rewrite $\log_{6} (c^{5} \sqrt[3]{a})$ as $\log_{6} (c^{5}) + \log_{6} (\sqrt[3]{a})$ .

$\log_{6} (c^{5}) + \log_{6} (\sqrt[3]{a})$

Step 2

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

$\log_{6} (c^{5}) + \log_{6} (a^{\frac{1}{3}})$

Step 3

Expand $\log_{6} (c^{5})$ by moving $5$ outside the logarithm.

$5 \log_{6} (c) + \log_{6} (a^{\frac{1}{3}})$

Step 4

Expand $\log_{6} (a^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$5 \log_{6} (c) + \frac{1}{3} \log_{6} (a)$

Step 5

Combine $\frac{1}{3}$ and $\log_{6} (a)$ .

$5 \log_{6} (c) + \frac{\log_{6} (a)}{3}$