Precalculus Examples

$\ln (25) - 2 \ln (5)$

Step 1

Simplify each term.

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Step 1.1

Simplify $- 2 \ln (5)$ by moving $2$ inside the logarithm.

$\ln (25) - \ln (5^{2})$

Step 1.2

Raise $5$ to the power of $2$ .

$\ln (25) - \ln (25)$

Step 2

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

$\ln (\frac{25}{25})$

Step 3

Divide $25$ by $25$ .

$\ln (1)$

Step 4

The natural logarithm of $1$ is $0$ .

$0$