SOLUTION: Solve: Log x + log (x+6) = 3

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Question 737009: Solve:
Log x + log (x+6) = 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log(x) + log(x+6) = 3

log[(x)*(x+6)] = 3

x(x+6) = 10^3

x(x+6) = 1000

x^2+6x = 1000

x^2+6x-1000 = 0


Use the quadratic formula to solve for x

x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%286%29%2B-sqrt%28%286%29%5E2-4%281%29%28-1000%29%29%29%2F%282%281%29%29 Plug in a+=+1, b+=+6, c+=+-1000

x+=+%28-6%2B-sqrt%2836-%28-4000%29%29%29%2F%282%29

x+=+%28-6%2B-sqrt%2836%2B4000%29%29%2F%282%29

x+=+%28-6%2B-sqrt%284036%29%29%2F2

x+=+%28-6%2Bsqrt%284036%29%29%2F2 or x+=+%28-6-sqrt%284036%29%29%2F2

x+=+%28-6%2B2%2Asqrt%281009%29%29%2F2 or x+=+%28-6-2%2Asqrt%281009%29%29%2F2

Exact Solutions: x+=+-3%2Bsqrt%281009%29 or x+=+-3-sqrt%281009%29

Approximate Solutions: x+=+28.764760 or x+=+-34.764760