Question 31387: Solve the equation:
log(3+x)-log(x-3)=log 3
Answer by mukhopadhyay(490)   (Show Source):
You can put this solution on YOUR website! log(3+x)-log(x-3)=log 3
=>log[(x+3)(x-3)]=log 3
=>log (x^2-9)=log 3
=>x^2-9 = 3
=>x^2 = 12
=>x = sqrt(12) or x = -sqrt(12)
x cannot be anyone of them because log(x-3) and log(x+3) are valid as long as (x-3) is not negative and (x+3) is not negative.
(x-3) is negative if x = sqrt(12) or x = -sqrt(12)
So, the answer is x has a null set
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