Precalculus Examples

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

Step 1

Expand $\ln ({(x^{3} e)}^{2 x})$ by moving $2 x$ outside the logarithm.

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

Step 2

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

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

Step 3

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

$2 x (3 \ln (x) + \ln (e))$

Step 4

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

$2 x (3 \ln (x) + 1)$

Step 5

Apply the distributive property.

$2 x (3 \ln (x)) + 2 x \cdot 1$

Step 6

Multiply $3$ by $2$ .

$6 x \ln (x) + 2 x \cdot 1$

Step 7

Multiply $2$ by $1$ .

$6 x \ln (x) + 2 x$