Precalculus Examples

$\log_{3} (\frac{\sqrt[4]{x}}{a^{2}})$

Step 1

Rewrite $\log_{3} (\frac{\sqrt[4]{x}}{a^{2}})$ as $\log_{3} (\sqrt[4]{x}) - \log_{3} (a^{2})$ .

$\log_{3} (\sqrt[4]{x}) - \log_{3} (a^{2})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x}$ as $x^{\frac{1}{4}}$ .

$\log_{3} (x^{\frac{1}{4}}) - \log_{3} (a^{2})$

Step 3

Expand $\log_{3} (x^{\frac{1}{4}})$ by moving $\frac{1}{4}$ outside the logarithm.

$\frac{1}{4} \log_{3} (x) - \log_{3} (a^{2})$

Step 4

Expand $\log_{3} (a^{2})$ by moving $2$ outside the logarithm.

$\frac{1}{4} \log_{3} (x) - (2 \log_{3} (a))$

Step 5

Multiply $2$ by $- 1$ .

$\frac{1}{4} \log_{3} (x) - 2 \log_{3} (a)$

Step 6

Combine $\frac{1}{4}$ and $\log_{3} (x)$ .

$\frac{\log_{3} (x)}{4} - 2 \log_{3} (a)$