Solve the logarithmic equation lnx - ln(x+1) = 2?

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ln x -ln (x+1) = 2

since ln x-ln y = ln x/y

then ln(x/(x+1)= 2

==> e^2 = x/(x+1)

==> (x+1)e^2 = X

==> xe^2 + e^2 = x

==> xe^2 -x= -e^2

==> x(e^2-1) = - e^2

==> x = -e^2/(e^2 -1)

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