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Math Help - Domain of log function

  1. #1
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    Domain of log function

    How do I find the domain of log10 (x^2 - 4)?
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  2. #2
    Super Member Bacterius's Avatar
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    What is the domain is the base 10 logarithm ? It is 0. Therefore, the domain of this function is :

    x^2 - 4 \geq 0
    x^2 \geq 4
    x \geq 2 OR x \leq -2

    Therefore, the domain of this function is x \leq -2 and x \geq 2
    Last edited by mr fantastic; November 10th 2009 at 03:54 AM. Reason: Fixed a bit of latex
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  3. #3
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    Quote Originally Posted by Bacterius View Post
    What is the domain is the base 10 logarithm ? It is 0. Therefore, the domain of this function is :

    x^2 - 4 \geq 0
    x^2 \geq 4
    x \geq 2 OR [tex]x \leq -2[\MATH]

    Therefore, the domain of this function is x \leq -2 and x \geq 2
    What is log_{10}(0)?

    The restriction over the logarithmic function is that its argument (what is "inside" it) must be strictly positive. So in this case, the requirement is that x^2-4 > 0 \Rightarrow |x| > 2 \Rightarrow x>2, x<-2
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  4. #4
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    Quote Originally Posted by Bacterius View Post
    What is the domain is the base 10 logarithm ? It is 0.
    Surely you mean "x> 0".

    Therefore, the domain of this function is :

    x^2 - 4 \geq 0
    x^2 \geq 4
    x \geq 2 OR [tex]x \leq -2[\MATH]

    Therefore, the domain of this function is x \leq -2 and x \geq 2
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  5. #5
    Super Member Bacterius's Avatar
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    Yes sorry I meant x \geq 0.
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  6. #6
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    Quote Originally Posted by Bacterius View Post
    Yes sorry I meant x \geq 0.
    Again, x>0, not \geq :P
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  7. #7
    Super Member Bacterius's Avatar
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    Oh my mistake, sorry. It is indeed x > 0
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