The domain of a log is .
I missed a lesson on the product and quotient laws for logarithms and am having a little trouble figuring out the restrictions.
For example:
Log (x^2+7x+12) - Log (x^2-9)
= Log (x+3)(x+4) - Log (x-3)(x+3)
= Log [(x+3)(x+4)]/(x-3)(x+3)]
= Log (x+4)/(x-3)
How would I go about finding the restrictions on this logarithm?
I know in total, there are three possibilities: x>-3, x>-4, x>3
And in the back of the book, it shows that x>3 is the only restriction.
What I tried was to plug in each restriction into each separate log to see if it worked, but when I tried it that way I found that both x>3 and x>-4 worked, and that conflicts with the answer in the back of the book.
All help greatly appreciated!
That's what I was thinking, but the back of the book doesn't include that as a restriction.
So to find the restrictions, I have to take all the possible restrictions and the final answer will include the restrictions which will not result in a negative inside the logarithm?