Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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