Precalculus Examples

$(\frac{1}{3}) \ln (4 - 1) - \frac{1}{3} \ln (2)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Subtract $1$ from $4$ .

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

Step 1.2

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

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

Step 1.3

Multiply $- \frac{1}{3} \ln (2)$ .

Tap for more steps...

Step 1.3.1

Reorder $\ln (2)$ and $\frac{1}{3}$ .

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

Step 1.3.2

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

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

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.13515503 \dots$