Calculus Examples

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

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

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

Step 2

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

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

Step 3

Cancel the common factor of $\ln (e)$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $2$ by $1$ .

$\ln (2)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (2)$

Decimal Form:

$0.69314718 \dots$