Precalculus Examples

$\log_{3} (\sqrt[3]{6})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{6}$ as $6^{\frac{1}{3}}$ .

$\log_{3} (6^{\frac{1}{3}})$

Step 2

Expand $\log_{3} (6^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{3} (6)$

Step 3

Rewrite $\log_{3} (6)$ as $\log_{3} (2 (3))$ .

$\frac{1}{3} \log_{3} (2 (3))$

Step 4

Rewrite $\log_{3} (2 (3))$ as $\log_{3} (2) + \log_{3} (3)$ .

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

Step 5

Logarithm base $3$ of $3$ is $1$ .

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

Step 6

Apply the distributive property.

$\frac{1}{3} \log_{3} (2) + \frac{1}{3} \cdot 1$

Step 7

Combine $\frac{1}{3}$ and $\log_{3} (2)$ .

$\frac{\log_{3} (2)}{3} + \frac{1}{3} \cdot 1$

Step 8

Multiply $\frac{1}{3}$ by $1$ .

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