I was doing my homework, when I came upon a question which has me a bit puzzled. The equation is quite simple, and is as follows:

log (x + 6) = 2 log x

So, I immediately rewrite this as:

x + 6 = x^2

Subtract x^2 from both sides, and then multiply both sides by -1 to turn it into a quadratic equality equation:

x^2-x-6=0

I run it through the quadratic formula, and get that x=-2 or 3.

However, the book says that the answer should only be 3, not -2. This made me think that maybe a log couldnt have a negative in it at all, which made me scratch my head a bit. I know that you cant flat out have a negative log. However, since it would be 2 log -2, and that would turn into -2^2, I dont see the problem, because the end result would be log 4. Am I completely wrong here? I was never taught that a log could not have a negative at all, but only that the end result could not have a log in the forum of "log - whatever."