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

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Question 166689: log3(x-2)+log3(x+4)=3
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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: