Answer
$x=3.303$
Work Step by Step
$\ln(x+1)-\ln(x-2)=\ln x$
$\ln\frac{x+1}{x-2}=\ln x$
Using the One-to-One Property:
$\frac{x+1}{x-2}=x$
$x+1=x^2-2x$
$0=x^2-3x-1~~$ ($a=1,b=-3,c=-1$):
$x=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-(-3)±\sqrt {(-3)^2-4(1)(-1)}}{2(1)}=\frac{3±\sqrt {13}}{2}$
$x=\frac{3+\sqrt {13}}{2}=3.303$
$x=\frac{3-\sqrt {13}}{2}=-0.303$. But since $-0.303$ is not in the domain of $\ln x$, it is not a valid solution.
