Solve {l}{1/2ln(x-1)+}{+1/2ln|x+1|}

$$\left. \begin{array} { l } { \frac { 1 } { 2 } \ln ( x - 1 ) + } \\ { + \frac { 1 } { 2 } \ln | x + 1 | } \end{array} \right.$$

Factor

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

Solution Steps

Factor out \frac{1}{2}.

$$\frac{\log_{e}\left(x-1\right)+\log_{e}\left(|x+1|\right)}{2}$$

Consider \ln(x-1)\times \frac{1}{\ln(e)}+\ln(|x+1|)\times \frac{1}{\ln(e)}. Factor out \frac{1}{\ln(e)}.

$$\frac{\ln(x-1)+\ln(|x+1|)}{\ln(e)}$$

Rewrite the complete factored expression.

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

Evaluate

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