Precalculus Examples

$\log (x) - \frac{1}{2} \log (x - 9)$

Step 1

Multiply $- \frac{1}{2} \log (x - 9)$ .

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Step 1.1

Reorder $\log (x - 9)$ and $\frac{1}{2}$ .

$\log (x) - (\frac{1}{2} \log (x - 9))$

Step 1.2

Simplify $\frac{1}{2} \log (x - 9)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (x) - \log ({(x - 9)}^{\frac{1}{2}})$

Step 2

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

$\log (\frac{x}{{(x - 9)}^{\frac{1}{2}}})$