SOLUTION: log3(x-2)+log3(x+4)=3

Question 166689: log3(x-2)+log3(x+4)=3
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
log3(x-2)+log3(x+4)=3
log3[(x-2)(x+4)]=3
(x-2)(x+4)=3^3
x^2+4x-2x-8 = 9
x^2+2x-8 = 9
x^2+2x-17 = 0
.
Since we can't factor, we must use the quadratic equation.
Do so will yield:
x = {3.243, -5.243}
.
Details here:

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=72 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.24264068711928, -5.24264068711928. Here's your graph:

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