SOLUTION: {{{ log ( 3, ( x- 2) ) + log (3, ( x- 4) ) = 2 }}}

Question 200476:
Found 2 solutions by nerdybill, cordereal:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Applying log rules:

Solving for x using the quadratic equation yields:
x = {6.162, -0.162}
We can throw out the negative solution leaving:
x = 6.162
.
Details of quadratic follows:

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=40 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.16227766016838, -0.16227766016838. Here's your graph:

Answer by cordereal(6) (Show Source): You can put this solution on YOUR website!
6.16227766016838, -0.16227766016838
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