Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \ln (2)$ by moving $3$ inside the logarithm.

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

Step 1.2

Raise $2$ to the power of $3$ .

$\ln (8) - \ln (\frac{1}{2})$

Step 2

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

$\ln (\frac{8}{\frac{1}{2}})$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\ln (8 \cdot 2)$

Step 4

Multiply $8$ by $2$ .

$\ln (16)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\ln (16)$

Decimal Form:

$2.77258872 \dots$