SOLUTION: Solve for x log (x)+log (x+3)=9 x=___

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Question 1153463: Solve for x
log (x)+log (x+3)=9
x=___
Answer by math_helper(2461) About Me  (Show Source):
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log(x) + log(x+3) = 9



Using log(a)+log(b) = log(ab)



  log(x(x+3)) = 9



Raise 10 to both sides



     x(x+3) = +10%5E9+

 

Expand and simplify:

+x%5E2+%2B+3x+-+10%5E9+=+0+



Use quadratic formula:

+x+=+%281%2F2%29%28-3+%2B-+sqrt%284000000009%29%29+



Discard negative solution



+x+=+%281%2F2%29%28-3+%2B+sqrt%284000000009%29%29+ ==>  (approx) +x+=+highlight%2831621.28%29+





Check:

log(31621.28) + log(3+31621.28) = 4.49998 + 4.50002 = 9   (ok, to within 5 decimal places)



EDIT: Added leading 1/2 which was omitted from typing only, not from the calculations