SOLUTION: ln x + ln (x-2) = 1

Question 427145: ln x + ln (x-2) = 1
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Applying log rules:
ln x + ln (x-2) = 1
ln x(x-2) = 1
x(x-2) = e^1
x^2-2x = e^1
x^2-2x - e^1 = 0
x^2-2x - 2.718 = 0
applying the quadratic formula we get:
x = {2.928, -0.928}
you can throw out the negative solution leaving:
x = 2.928
.
details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=14.872 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.92821160664487, -0.928211606644872. Here's your graph:

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