SOLUTION: Solve for x: 2 ln x - ln (x+1) = 3 Can someone please solve this problem step by step for me and explain how and why it is solved a certain way? Thank you!

Question 1025485: Solve for x: 2 ln x - ln (x+1) = 3
Can someone please solve this problem step by step for me and explain how and why it is solved a certain way? Thank you!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve for x: 2 ln x - ln (x+1) = 3
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ln(x^2) - ln(x+1) = 3
ln(x^2) = ln(x+1) + 3
ln(x^2) = ln(x+1) + ln(e^3)
ln(x^2) = ln(e^3*(x+1))
x^2 = e^3*x+1
x^2 - e^3x - 1 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=407.428793492736 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 20.135201189791, -0.0496642666032567. Here's your graph:

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The negative solution is not allowed due to ln(x).
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email any questions about the method via the TY note.

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