Precalculus Examples

$3 \ln (5) - \ln (2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \ln (5)$ by moving $3$ inside the logarithm.

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

Step 1.2

Raise $5$ to the power of $3$ .

$\ln (125) - \ln (2)$

Step 2

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

$\ln (\frac{125}{2})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{125}{2})$

Decimal Form:

$4.13516655 \dots$