Precalculus Examples

$2 \ln (\sqrt{x} e^{x})$

Step 1

Rewrite $\ln (\sqrt{x} e^{x})$ as $\ln (\sqrt{x}) + \ln (e^{x})$ .

$2 (\ln (\sqrt{x}) + \ln (e^{x}))$

Step 2

Use logarithm rules to move $x$ out of the exponent.

$2 (\ln (\sqrt{x}) + x \ln (e))$

Step 3

The natural logarithm of $e$ is $1$ .

$2 (\ln (\sqrt{x}) + x \cdot 1)$

Step 4

Multiply $x$ by $1$ .

$2 (\ln (\sqrt{x}) + x)$

Step 5

Apply the distributive property.

$2 \ln (\sqrt{x}) + 2 x$

Step 6

Reorder $2 \ln (\sqrt{x})$ and $2 x$ .

$2 x + 2 \ln (\sqrt{x})$