Precalculus Examples

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

Step 1

Rewrite $\ln (x^{2} e^{x})$ as $\ln (x^{2}) + \ln (e^{x})$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply $x$ by $1$ .

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

Step 5

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

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