Answer
The solution set is $\{ \frac{2}{e^2-1}\approx0.31 \}$.
Work Step by Step
The given equation is
$\ln (x+2) -\ln x=2$
Add $\ln (x)$ to both sides.
$\ln (x+2) -\ln x+\ln x=2+\ln x$
Use $2=\ln e^2 $.
$\ln (x+2) =\ln e^2+\ln x$
Use product rule on the right hand side.
$\ln (x+2) =\ln (e^2x)$
$ x+2 =e^2x$
Isolate $x$.
$x=\frac{2}{e^2-1}$
$x=0.31$.
