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) = 

 

Expand and simplify:





Use quadratic formula:





Discard negative solution



 ==>  (approx) 





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 

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