Precalculus Examples

$4 \log (0.0001) - 3 \ln (\sqrt[4]{e})$

Step 1

Log base $10$ of $0.0001$ is approximately $- 4$ .

$4 \cdot - 4 - 3 \ln (\sqrt[4]{e})$

Step 2

Multiply $4$ by $- 4$ .

$- 16 - 3 \ln (\sqrt[4]{e})$

Step 3

Simplify $- 3 \ln (\sqrt[4]{e})$ by moving $3$ inside the logarithm.

$- 16 - \ln ({\sqrt[4]{e}}^{3})$

Step 4

Rewrite ${\sqrt[4]{e}}^{3}$ as $\sqrt[4]{e^{3}}$ .

$- 16 - \ln (\sqrt[4]{e^{3}})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 16 - \ln (\sqrt[4]{e^{3}})$

Decimal Form:

$- 16.75$