SOLUTION: log(x)+log(x+3)=log(10)

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Question 870642: log(x)+log(x+3)=log(10)
Answer by jim_thompson5910(35256) About Me  (Show Source):
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log(x)+log(x+3)=log(10)


log(x*(x+3))=log(10)


10^[log(x*(x+3))]=10^[log(10)]


x*(x+3) = 10


x^2+3x = 10


x^2+3x-10 = 0


(x + 5)(x - 2) = 0


x + 5 = 0 or x - 2 = 0


x = -5 or x = 2


The domain of log(x) is x > 0, so we toss x = -5.


The only solution is x = 2.