Precalculus Examples

$\ln (e^{3 x} (x^{2} + 1))$

Step 1

Rewrite $\ln (e^{3 x} (x^{2} + 1))$ as $\ln (e^{3 x}) + \ln (x^{2} + 1)$ .

$\ln (e^{3 x}) + \ln (x^{2} + 1)$

Step 2

Expand $\ln (e^{3 x})$ by moving $3 x$ outside the logarithm.

$3 x \ln (e) + \ln (x^{2} + 1)$

Step 3

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

$3 x \cdot 1 + \ln (x^{2} + 1)$

Step 4

Multiply $3$ by $1$ .

$3 x + \ln (x^{2} + 1)$