Precalculus Examples

\ln (\frac{1}{e^{4}})

$\ln (\frac{1}{e^{4}})$

Step 1

Move

e^{4}

$e^{4}$ to the numerator using the negative exponent rule

\frac{1}{b^{n}} = b^{- n}

$\frac{1}{b^{n}} = b^{- n}$ .

\ln (e^{- 4})

$\ln (e^{- 4})$

Step 2

Expand

\ln (e^{- 4})

$\ln (e^{- 4})$ by moving

- 4

$- 4$ outside the logarithm.

- 4 \ln (e)

$- 4 \ln (e)$

Step 3

The natural logarithm of

e

$e$ is

1

$1$ .

- 4 \cdot 1

$- 4 \cdot 1$

Step 4

Multiply

- 4

$- 4$ by

1

$1$ .

- 4

$- 4$

Enter a problem...

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$