Domain of logarithmic funtion

6throute (x-7)
--------------
log11(13-x)



What is the domain of the function in interval notation.


I know to set x-7 > 0, so that gets me x>7 , and I know I have to set 13-x > 0, which gets me x < 13. But the notation that is correct is [7,12)U(12,13). Where do you get the 12 from?
 

tiny-tim

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Hi lwelch70! :smile:

(have a ≥ :wink:)
But the notation that is correct is [7,12)U(12,13). Where do you get the 12 from?
Hint: what's 1/log11(13 - 12) ? :wink:
 
Hi lwelch70! :smile:

(have a ≥ :wink:)


Hint: what's 1/log11(13 - 12) ? :wink:
I'm sorry but that just confused me. Haha.
 
Is it becuase it's in the denominator? So I won't be able to take the log of any base of 1 since that would give me 0 as a denominator?
 

tiny-tim

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[STRIKE]Well, the answer, [7,12)U(12,13), excludes the value 12 …

so pop it into the formula to see why!! :smile:[/STRIKE]

oops, you beat me to it! :biggrin:

Yes, you can't have something/0 :smile:
 
So if I would see this on a test, and am not given the correct answer (haha), I simply make surre that I am not taking log(anything that equals 1) in the denominator?
 

tiny-tim

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That's it! :smile:
 

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