Precalculus Examples

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

Step 1

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

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

Step 2

Factor $2$ out of $2 x - 6$ .

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Step 2.1

Factor $2$ out of $2 x$ .

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

Step 2.2

Factor $2$ out of $- 6$ .

$\log_{5} (\frac{x + 5}{2 x + 2 \cdot - 3})$

Step 2.3

Factor $2$ out of $2 x + 2 \cdot - 3$ .

$\log_{5} (\frac{x + 5}{2 (x - 3)})$