Precalculus Examples

$\ln (\ln (e^{e^{300}}))$

Step 1

Expand $\ln (e^{e^{300}})$ by moving $e^{300}$ outside the logarithm.

$\ln (e^{300} \ln (e))$

Step 2

Rewrite $\ln (e^{300} \ln (e))$ as $\ln (e^{300}) + \ln (\ln (e))$ .

$\ln (e^{300}) + \ln (\ln (e))$

Step 3

Use logarithm rules to move $300$ out of the exponent.

$300 \ln (e) + \ln (\ln (e))$

Step 4

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

$300 \cdot 1 + \ln (\ln (e))$

Step 5

Multiply $300$ by $1$ .

$300 + \ln (\ln (e))$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

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

$300 + \ln (1)$

Step 6.2

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

$300 + 0$

Step 7

Add $300$ and $0$ .

$300$