Precalculus Examples

$\log_{3} (\sqrt[5]{x} \cdot y)$

Step 1

Rewrite $\log_{3} (\sqrt[5]{x} \cdot y)$ as $\log_{3} (\sqrt[5]{x}) + \log_{3} (y)$ .

$\log_{3} (\sqrt[5]{x}) + \log_{3} (y)$

Step 2

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

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

Step 3

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

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

Step 4

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

$\frac{\log_{3} (x)}{5} + \log_{3} (y)$