Precalculus Examples

$12 \log (x + 9) - 4 \log (x)$

Step 1

Simplify each term.

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Step 1.1

Simplify $12 \log (x + 9)$ by moving $12$ inside the logarithm.

$\log ({(x + 9)}^{12}) - 4 \log (x)$

Step 1.2

Simplify $- 4 \log (x)$ by moving $4$ inside the logarithm.

$\log ({(x + 9)}^{12}) - \log (x^{4})$

Step 2

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

$\log (\frac{{(x + 9)}^{12}}{x^{4}})$