Precalculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

The natural logarithm of $1$ is $0$ .

$\frac{\ln (3) - 0}{3}$

Step 1.2

Multiply $- 1$ by $0$ .

$\frac{\ln (3) + 0}{3}$

Step 1.3

Add $\ln (3)$ and $0$ .

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

Step 2

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

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

Step 3

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.36620409 \dots$