## Functions Modeling Change: A Preparation for Calculus, 5th Edition

$\frac{1}{2}(\ln(x-1)-\ln(x+1))$
First, use the fact that $\ln a^b=b \ln a$ and $\sqrt{a}=a^{\frac{1}{2}}$ to simplify the expression to $\frac{1}{2} \ln{\frac{x-1}{x+1}}.$ Since $\log(a/b)=\log(a)-\log(b)$, the expression can be simplified to $\frac{1}{2}(\ln(x-1)-\ln(x+1))$.