Precalculus Examples

$5 \log_{2} (x - 6) - 7 \log_{2} (x + 9)$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log_{2} (x - 6)$ by moving $5$ inside the logarithm.

$\log_{2} ({(x - 6)}^{5}) - 7 \log_{2} (x + 9)$

Step 1.2

Simplify $- 7 \log_{2} (x + 9)$ by moving $7$ inside the logarithm.

$\log_{2} ({(x - 6)}^{5}) - \log_{2} ({(x + 9)}^{7})$

Step 2

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

$\log_{2} (\frac{{(x - 6)}^{5}}{{(x + 9)}^{7}})$