Precalculus Examples

$8 \log (\sqrt[4]{x})$

Step 1

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

$8 \log (x^{\frac{1}{4}})$

Step 2

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

$8 (\frac{1}{4} \log (x))$

Step 3

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

$8 \frac{\log (x)}{4}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Factor $4$ out of $8$ .

$4 (2) \frac{\log (x)}{4}$

Step 4.2

Cancel the common factor.

$4 \cdot 2 \frac{\log (x)}{4}$

Step 4.3

Rewrite the expression.

$2 \log (x)$