Calculus Examples

$\ln (4 e)$

Step 1

Rewrite $\ln (4 e)$ as $\ln (4) + \ln (e)$ .

$\ln (4) + \ln (e)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

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

Step 2.2

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

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

Step 2.3

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

$2 \ln (2) + 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \ln (2) + 1$

Decimal Form:

$2.38629436 \dots$