Precalculus Examples

$2 \ln (x) - \ln (x - 1) + \ln (x + 1)$

Step 1

Simplify $2 \ln (x)$ by moving $2$ inside the logarithm.

$\ln (x^{2}) - \ln (x - 1) + \ln (x + 1)$

Step 2

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

$\ln (\frac{x^{2}}{x - 1}) + \ln (x + 1)$

Step 3

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

$\ln (\frac{x^{2}}{x - 1} (x + 1))$

Step 4

Multiply $\frac{x^{2}}{x - 1}$ by $x + 1$ .

$\ln (\frac{x^{2} (x + 1)}{x - 1})$