SOLUTION: Log(2) (x-8) + Log(2) (x+4) = 5

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Question 172820: Log(2) (x-8) + Log(2) (x+4) = 5
Found 3 solutions by nerdybill, Alan3354, josmiceli:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website!
Apply log rules. Review them at:
http://www.purplemath.com/modules/logrules.htm
.
Log(2) (x-8) + Log(2) (x+4) = 5
Log(2) [(x-8)(x+4)] = 5
(x-8)(x+4) = 2^5
(x-8)(x+4) = 32
x^2-4x-32 = 32
x^2-4x-64 = 0
.
Since we can't factor, we must use the quadratic formula. Doing so yields:
x = {10.246, -6.246}
.
Details of quadratic below:

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=272 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10.2462112512353, -6.24621125123532. Here's your graph:

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
Log(2) (x-8) + Log(2) (x+4) = 5
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Assuming you mean log base 2:

Adding logs implies multiplying
(x-8)*(x+4)) = 2^5 = 32

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=272 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10.2462112512353, -6.24621125123532. Here's your graph:

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The negative answer won't work, so it's
2 + 2sqrt(17)

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!

answer
I'll check the answer

OK