Precalculus Examples

$\ln (\sqrt{x - 1})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 1}$ as ${(x - 1)}^{\frac{1}{2}}$ .

$\ln ({(x - 1)}^{\frac{1}{2}})$

Step 2

Expand $\ln ({(x - 1)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \ln (x - 1)$

Step 3

Combine $\frac{1}{2}$ and $\ln (x - 1)$ .

$\frac{\ln (x - 1)}{2}$