Precalculus Examples

$4 \log_{b} (y - 7) - 6 \log_{b} (y + 5)$

Step 1

Simplify each term.

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Step 1.1

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

$\log_{b} ({(y - 7)}^{4}) - 6 \log_{b} (y + 5)$

Step 1.2

Simplify $- 6 \log_{b} (y + 5)$ by moving $6$ inside the logarithm.

$\log_{b} ({(y - 7)}^{4}) - \log_{b} ({(y + 5)}^{6})$

Step 2

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

$\log_{b} (\frac{{(y - 7)}^{4}}{{(y + 5)}^{6}})$