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.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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.       Log On


   

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(35256) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-41+=+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=%280%29%5E2-4%2A1%2A-41=164.

Discriminant d=164 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+164+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+164+%29%29%2F2%5C1+=+6.40312423743285
x%5B2%5D+=+%28-%280%29-sqrt%28+164+%29%29%2F2%5C1+=+-6.40312423743285

Quadratic expression 1x%5E2%2B0x%2B-41 can be factored:
1x%5E2%2B0x%2B-41+=+1%28x-6.40312423743285%29%2A%28x--6.40312423743285%29
Again, the answer is: 6.40312423743285, -6.40312423743285. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-41+%29


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