Precalculus Examples

$\log_{4} (\sqrt{x^{3}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{3}}$ as $x^{\frac{3}{2}}$ .

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

Step 2

Expand $\log_{4} (x^{\frac{3}{2}})$ by moving $\frac{3}{2}$ outside the logarithm.

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

Step 3

Combine $\frac{3}{2}$ and $\log_{4} (x)$ .

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