Solve ln(x)-1/2ln(x^2+1)

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

Factor

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

Solution Steps

Factor out \frac{1}{2}.

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

Consider 2\ln(x)\times \frac{1}{\ln(e)}-\ln(x^{2}+1)\times \frac{1}{\ln(e)}. Factor out \frac{1}{\ln(e)}.

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

Rewrite the complete factored expression.

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

Evaluate

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