Precalculus Examples

$\log_{7} (\sqrt[3]{x^{2} + 9})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2} + 9}$ as ${(x^{2} + 9)}^{\frac{1}{3}}$ .

$\log_{7} ({(x^{2} + 9)}^{\frac{1}{3}})$

Step 2

Expand $\log_{7} ({(x^{2} + 9)}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{7} (x^{2} + 9)$

Step 3

Combine $\frac{1}{3}$ and $\log_{7} (x^{2} + 9)$ .

$\frac{\log_{7} (x^{2} + 9)}{3}$