Precalculus Examples

$4 \log_{8} (x - 7) - 5 \log_{8} (x + 5)$

Step 1

Simplify each term.

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Step 1.1

Simplify $4 \log_{8} (x - 7)$ by moving $4$ inside the logarithm.

$\log_{8} ({(x - 7)}^{4}) - 5 \log_{8} (x + 5)$

Step 1.2

Simplify $- 5 \log_{8} (x + 5)$ by moving $5$ inside the logarithm.

$\log_{8} ({(x - 7)}^{4}) - \log_{8} ({(x + 5)}^{5})$

Step 2

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

$\log_{8} (\frac{{(x - 7)}^{4}}{{(x + 5)}^{5}})$