Precalculus Examples

$2 \log (x) - 6 \log (x - 9)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log (x)$ by moving $2$ inside the logarithm.

$\log (x^{2}) - 6 \log (x - 9)$

Step 1.2

Simplify $- 6 \log (x - 9)$ by moving $6$ inside the logarithm.

$\log (x^{2}) - \log ({(x - 9)}^{6})$

Step 2

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

$\log (\frac{x^{2}}{{(x - 9)}^{6}})$