Precalculus Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

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

Step 1.2

Simplify $- 2 \ln (x + 1)$ by moving $2$ inside the logarithm.

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

Step 2

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

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