SOLUTION: lnx + ln (x+3) = 1

Question 386020: lnx + ln (x+3) = 1
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
lnx + ln (x+3) = 1
ln x(x+3) = 1
x(x+3) = e^1
x^2+3x = e^1
x^2+3x-e = 0
x^2+3x-2.7183 = 0
Applying the "quadratic formula" we get:
x= {0.728968371242625, -3.72896837124262}
Throw out the negative solution (extraneous) which leaves us with:
x = 0.729
.
Details of quadratic to follow:
.

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=19.8732 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.728968371242625, -3.72896837124262. Here's your graph:

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