How would I solve for x in this problem?

Question

ln x - ln(x+1) = 1

Answer 1

quotient rule!

lnx - ln(x+1) = 1 ---------->

ln((x/(x+1)) = 1        

next (def of logarithms)

e^1 = x/(x+1)

(x+1)e = x

ex -x = -e

x(e-1) = -e

x = -e/(e-1) OR e/(1-e)

however this answer does not work in the original equation because it's negative and you can't take logs of negatives (for a real answer). So, NO SOLUTION

Answer 2

ln ((x/(x+1))=ln e

ex=x+1

x=1/(e-1)

Answer 3

ln(x) - ln(x+1) = 1

ln[x / (x+1)] = 1

x / (x + 1) = e

x = ex + e

and so forth