Precalculus Examples

$\frac{1}{2} \cdot \ln (3) - \frac{1}{2} \cdot \ln (5)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (3^{\frac{1}{2}}) - \frac{1}{2} \cdot \ln (5)$

Step 1.2

Multiply $- \frac{1}{2} \ln (5)$ .

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Step 1.2.1

Reorder $\ln (5)$ and $\frac{1}{2}$ .

$\ln (3^{\frac{1}{2}}) - (\frac{1}{2} \ln (5))$

Step 1.2.2

Simplify $\frac{1}{2} \ln (5)$ by moving $\frac{1}{2}$ inside the logarithm.

$\ln (3^{\frac{1}{2}}) - \ln (5^{\frac{1}{2}})$

Step 2

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

$\ln (\frac{3^{\frac{1}{2}}}{5^{\frac{1}{2}}})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{3^{\frac{1}{2}}}{5^{\frac{1}{2}}})$

Decimal Form:

$- 0.25541281 \dots$