Precalculus Examples

$\log_{27} (\sqrt[3]{1 - x})$

Step 1

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

$\log_{27} ({(1 - x)}^{\frac{1}{3}})$

Step 2

Expand $\log_{27} ({(1 - x)}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{27} (1 - x)$

Step 3

Combine $\frac{1}{3}$ and $\log_{27} (1 - x)$ .

$\frac{\log_{27} (1 - x)}{3}$