SOLUTION: here is a question I have had some difficulty with as far as order of operations go on the calculator... log 6(x-5)+log 6x=2 Any help would be greatly appreciated

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Question 555740: here is a question I have had some difficulty with as far as order of operations go on the calculator...
log 6(x-5)+log 6x=2
Any help would be greatly appreciated
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
log 6(x-5)+log 6x=2
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Adding logs --> multiply
I think you mean base 6.
log%286%2Cx%28x-5%29%29+=+2
x(x-5) = 36
x%5E2+-+5x+-+36+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B-36+=+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=%28-5%29%5E2-4%2A1%2A-36=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%28-5%29-sqrt%28+169+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B-5x%2B-36 can be factored:
1x%5E2%2B-5x%2B-36+=+%28x-9%29%2A%28x--4%29
Again, the answer is: 9, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-36+%29

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x = -4 won't work
x = 9
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I didn't use a calculator.