Precalculus Examples

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

Step 1

Factor out $e^{2}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $\ln (e \sqrt{e})$ as $\ln (e) + \ln (\sqrt{e})$ .

$\ln (e) + \ln (\sqrt{e})$

Step 4

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

$1 + \ln (\sqrt{e})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$1 + \ln (\sqrt{e})$

Decimal Form:

$1.5$