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Homework Help: Domain of logarithmic funtion

  1. Dec 13, 2009 #1
    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?
     
  2. jcsd
  3. Dec 13, 2009 #2

    tiny-tim

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    Hi lwelch70! :smile:

    (have a ≥ :wink:)
    Hint: what's 1/log11(13 - 12) ? :wink:
     
  4. Dec 13, 2009 #3
    I'm sorry but that just confused me. Haha.
     
  5. Dec 13, 2009 #4
    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?
     
  6. Dec 13, 2009 #5

    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:
     
  7. Dec 13, 2009 #6
    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?
     
  8. Dec 13, 2009 #7

    tiny-tim

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    That's it! :smile:
     
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