SOLUTION: log3x+log(x+2)=1

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Question 192261: log3x+log(x+2)=1
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
log3x+log(x+2)=1
log3x(x+2)=1
3x(x+2)=10^1
3x^2+6x=10
3x^2+6x-10=0
Solving the above using the quadratic equation yields two solutions:
x = {1.082, -3.082}
.
Details of quadratic follows:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B6x%2B-10+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A3%2A-10=156.

Discriminant d=156 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+156+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+156+%29%29%2F2%5C3+=+1.08166599946613
x%5B2%5D+=+%28-%286%29-sqrt%28+156+%29%29%2F2%5C3+=+-3.08166599946613

Quadratic expression 3x%5E2%2B6x%2B-10 can be factored:
3x%5E2%2B6x%2B-10+=+3%28x-1.08166599946613%29%2A%28x--3.08166599946613%29
Again, the answer is: 1.08166599946613, -3.08166599946613. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B6%2Ax%2B-10+%29