Precalculus Examples

$4 \ln (x + 2) - 9 \ln (x)$

Step 1

Simplify each term.

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Step 1.1

Simplify $4 \ln (x + 2)$ by moving $4$ inside the logarithm.

$\ln ({(x + 2)}^{4}) - 9 \ln (x)$

Step 1.2

Simplify $- 9 \ln (x)$ by moving $9$ inside the logarithm.

$\ln ({(x + 2)}^{4}) - \ln (x^{9})$

Step 2

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

$\ln (\frac{{(x + 2)}^{4}}{x^{9}})$