Precalculus Examples

$e \ln (\sqrt{x})$

Step 1

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

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

Step 2

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

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

Step 3

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

$e \frac{\ln (x)}{2}$

Step 4

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

$\frac{e \ln (x)}{2}$