Precalculus Examples

$\frac{1}{6} \cdot \ln (8) - \frac{1}{6} \cdot \ln (4)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{6} \ln (8)$ by moving $\frac{1}{6}$ inside the logarithm.

$\ln (8^{\frac{1}{6}}) - \frac{1}{6} \cdot \ln (4)$

Step 1.2

Multiply $- \frac{1}{6} \ln (4)$ .

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Step 1.2.1

Reorder $\ln (4)$ and $\frac{1}{6}$ .

$\ln (8^{\frac{1}{6}}) - (\frac{1}{6} \ln (4))$

Step 1.2.2

Simplify $\frac{1}{6} \ln (4)$ by moving $\frac{1}{6}$ inside the logarithm.

$\ln (8^{\frac{1}{6}}) - \ln (4^{\frac{1}{6}})$

Step 2

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

$\ln (\frac{8^{\frac{1}{6}}}{4^{\frac{1}{6}}})$

Step 3

Use the power of quotient rule $\frac{a^{m}}{b^{m}} = {(\frac{a}{b})}^{m}$ .

$\ln ({(\frac{8}{4})}^{\frac{1}{6}})$

Step 4

Divide $8$ by $4$ .

$\ln (2^{\frac{1}{6}})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\ln (2^{\frac{1}{6}})$

Decimal Form:

$0.11552453 \dots$