Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Use logarithm rules to move $2$ out of the exponent.

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

Step 4

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

$2 \cdot 1 + \ln (\ln (e))$

Step 5

Multiply $2$ by $1$ .

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

Step 6

Simplify each term.

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Step 6.1

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

$2 + \ln (1)$

Step 6.2

The natural logarithm of $1$ is $0$ .

$2 + 0$

Step 7

Add $2$ and $0$ .

$2$