Calculus Examples

$\ln (\sqrt{e^{6}})$

Step 1

Rewrite $e^{6}$ as ${(e^{3})}^{2}$ .

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

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$\ln (e^{3})$

Step 3

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

$3 \ln (e)$

Step 4

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

$3 \cdot 1$

Step 5

Multiply $3$ by $1$ .

$3$