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

Question 39229This question is from textbook Algebra 2
: Ln(x)+Ln(x-2)=1 This question is from textbook Algebra 2

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Ln(x)+Ln(x-2)=1
Ln((x)(x-2))=1
Ln(x^2-2x)=1
x^2-2x=e
x^2-2x-e=0
Looks a little like what is below. No solutions exist.

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 : .

The discriminant -6.873127312 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -6.873127312 is + or - .

The solution is

Here's your graph:

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