Precalculus Examples

$\frac{\ln (\frac{1}{2})}{3}$

Step 1

Rewrite $\frac{\ln (\frac{1}{2})}{3}$ as $\frac{1}{3} \ln (\frac{1}{2})$ .

$\frac{1}{3} \ln (\frac{1}{2})$

Step 2

Simplify $\frac{1}{3} \ln (\frac{1}{2})$ by moving $\frac{1}{3}$ inside the logarithm.

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

Step 3

Apply the product rule to $\frac{1}{2}$ .

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

Step 4

One to any power is one.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.23104906 \dots$