Precalculus Examples

$2 \ln (5) - 3 \ln (x) + \ln (x^{2} - 10)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (5^{2}) - 3 \ln (x) + \ln (x^{2} - 10)$

Step 1.2

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

$\ln (25) - 3 \ln (x) + \ln (x^{2} - 10)$

Step 1.3

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

$\ln (25) - \ln (x^{3}) + \ln (x^{2} - 10)$

Step 2

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

$\ln (\frac{25}{x^{3}}) + \ln (x^{2} - 10)$

Step 3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (\frac{25}{x^{3}} (x^{2} - 10))$

Step 4

Multiply $\frac{25}{x^{3}}$ by $x^{2} - 10$ .

$\ln (\frac{25 (x^{2} - 10)}{x^{3}})$