Evaluate natural log of e^5- natural log of e^2

$\ln (e^{5}) - \ln (e^{2})$

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

$\ln (\frac{e^{5}}{e^{2}})$

Cancel the common factor of $e^{5}$ and $e^{2}$ .

Factor $e^{2}$ out of $e^{5}$ .

$\ln (\frac{e^{2} e^{3}}{e^{2}})$

Cancel the common factors.

Multiply by $1$ .

$\ln (\frac{e^{2} e^{3}}{e^{2} \cdot 1})$

Cancel the common factor.

$\ln (\frac{e^{2} e^{3}}{e^{2} \cdot 1})$

Rewrite the expression.

$\ln (\frac{e^{3}}{1})$

Divide $e^{3}$ by $1$ .

$\ln (e^{3})$

Use logarithm rules to move $3$ out of the exponent.

$3 \ln (e)$

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

$3 \cdot 1$

Multiply $3$ by $1$ .

$3$