Precalculus Examples

$\ln (e^{5} x^{2})$

Step 1

Rewrite $\ln (e^{5} x^{2})$ as $\ln (e^{5}) + \ln (x^{2})$ .

$\ln (e^{5}) + \ln (x^{2})$

Step 2

Use logarithm rules to move $5$ out of the exponent.

$5 \ln (e) + \ln (x^{2})$

Step 3

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

$5 \cdot 1 + \ln (x^{2})$

Step 4

Multiply $5$ by $1$ .

$5 + \ln (x^{2})$