Precalculus Examples

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

Step 1

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

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

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

Step 3

Multiply $\frac{x}{2 x + 3}$ by $2 x - 3$ .

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