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

Expand $\ln (e^{5})$ by moving $5$ outside the logarithm.

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

Step 3

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

$5 \ln (e) + 2 \ln (x)$

Step 4

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

$5 \cdot 1 + 2 \ln (x)$

Step 5

Multiply $5$ by $1$ .

$5 + 2 \ln (x)$