Precalculus Examples

$\ln (x) - \ln (x + 2) + \ln (2 x - 3)$

Step 1

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

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

Step 2

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

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

Step 3

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

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