Answer
The solution set is $\{ \frac{1}{e-1}\approx 0.58 \}$.
Work Step by Step
The given equation is
$\ln (x+1) -\ln x=1$
Add $\ln (x)$ to both sides.
$\ln (x+1) -\ln x+\ln x=1+\ln x$
Use $1=\ln e $.
$\ln (x+1) =\ln e+\ln x$
Use product rule on the right hand side.
$\ln (x+1) =\ln (ex)$
$ x+1 =ex$
Isolate $x$.
$x=\frac{1}{e-1}$
$x=0.58$.
