Expand the Logarithmic Expression natural log of xe^x

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

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

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

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

$\ln (x) + x \ln (e)$

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

$\ln (x) + x \cdot 1$

Multiply $x$ by $1$ .

$\ln (x) + x$