Precalculus Examples

$\frac{1}{2} \cdot (\log_{5} (x - 8) - \log_{5} (x))$

Step 1

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

$\frac{1}{2} \cdot \log_{5} (\frac{x - 8}{x})$

Step 2

Simplify $\frac{1}{2} \log_{5} (\frac{x - 8}{x})$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{5} ({(\frac{x - 8}{x})}^{\frac{1}{2}})$

Step 3

Apply the product rule to $\frac{x - 8}{x}$ .

$\log_{5} (\frac{{(x - 8)}^{\frac{1}{2}}}{x^{\frac{1}{2}}})$