Precalculus Examples

$6 \log_{5} (y - 6) - 3 \log_{5} (y + 8)$

Step 1

Simplify each term.

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Step 1.1

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

$\log_{5} ({(y - 6)}^{6}) - 3 \log_{5} (y + 8)$

Step 1.2

Simplify $- 3 \log_{5} (y + 8)$ by moving $3$ inside the logarithm.

$\log_{5} ({(y - 6)}^{6}) - \log_{5} ({(y + 8)}^{3})$

Step 2

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

$\log_{5} (\frac{{(y - 6)}^{6}}{{(y + 8)}^{3}})$