SOLUTION: I need help with this problem: log3x+log(x+2)=1

Question 192244: I need help with this problem:
log3x+log(x+2)=1
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Apply "log rules":
log3x+log(x+2)=1
log(3x)(x+2)=1
(3x)(x+2)=10^1
3x^2+6x=10
3x^2+6x-10=0
Solve using the quadratic equation:
x = {1.082, -3.082}
We can toss out the negative solution leaving:
x = 1.082
.
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=156 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.08166599946613, -3.08166599946613. Here's your graph:

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