SOLUTION: How do u solve log (base 5)(x+4)+ log(base 5)(x-4)=2 I thought about combing the logs but i don't no what to do with the rest of the problem.

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Question 78707: How do u solve log (base 5)(x+4)+ log(base 5)(x-4)=2
I thought about combing the logs but i don't no what to do with the rest of the problem.
Answer by jim_thompson5910(21667) (Show Source):
You can put this solution on YOUR website!

Combine the logs

Rewrite the expression as this:

Foil and subtract 25 from both sides

Use the quadratic formula to solve for x

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=164 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.40312423743285, -6.40312423743285. Here's your graph:

Since the argument for logarithms cannot be negative, we must discard our negative answer.
So our answer is
x=6.40312423743285