Precalculus Examples

$\log_{8} (\sqrt[3]{x^{2} + 5})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2} + 5}$ as ${(x^{2} + 5)}^{\frac{1}{3}}$ .

$\log_{8} ({(x^{2} + 5)}^{\frac{1}{3}})$

Step 2

Expand $\log_{8} ({(x^{2} + 5)}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{8} (x^{2} + 5)$

Step 3

Combine $\frac{1}{3}$ and $\log_{8} (x^{2} + 5)$ .

$\frac{\log_{8} (x^{2} + 5)}{3}$