Precalculus Examples

$\log_{5} (\sqrt[3]{x^{2} + 1})$

Step 1

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

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

Step 2

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

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

Step 3

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

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