SOLUTION: I need help solving for x in this: ln (x+1) - ln (x) = 2. My options are 1/(e^2 - 1), x/(1-x), 1/x-1, e^2 - 1. Thanks!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I need help solving for x in this: ln (x+1) - ln (x) = 2. My options are 1/(e^2 - 1), x/(1-x), 1/x-1, e^2 - 1. Thanks!       Log On


   

Question 767554: I need help solving for x in this: ln (x+1) - ln (x) = 2. My options are 1/(e^2 - 1), x/(1-x), 1/x-1, e^2 - 1. Thanks!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x%2B1%29-ln%28x%29=ln%28%28x%2B1%29%2Fx%29 because a rule of logarithms allows this.

You then have ln%28%28x%2B1%29%2Fx%29=2
e%5E2=%28x%2B1%29%2Fx and the left member is a constant.
x%2Ae%5E2=x%2B1
-x%2Bx%2Ae%5E2=1
x%28-1%2Be%5E2%29=1
x=1%2F%28-1%2Be%5E2%29
or equivalently
x=1%2F%28e%5E2-1%29