Precalculus Examples

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

Step 1

Rewrite $\ln (\frac{5}{\sqrt{e^{5}}})$ as $\ln (5) - \ln (\sqrt{e^{5}})$ .

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

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{e^{5}}$ as $e^{\frac{5}{2}}$ .

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

Step 3

Expand $\ln (e^{\frac{5}{2}})$ by moving $\frac{5}{2}$ outside the logarithm.

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

Step 4

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

$\ln (5) - (\frac{5}{2} \cdot 1)$

Step 5

Multiply $\frac{5}{2}$ by $1$ .

$\ln (5) - \frac{5}{2}$