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Thread: 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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    Super Member Bacterius's Avatar
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    What is the domain is the base 10 logarithm ? It is $\displaystyle 0$. Therefore, the domain of this function is :

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

    Therefore, the domain of this function is $\displaystyle x \leq -2$ and $\displaystyle x \geq 2$
    Last edited by mr fantastic; Nov 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 $\displaystyle 0$. Therefore, the domain of this function is :

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

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

    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 $\displaystyle x^2-4 > 0 \Rightarrow |x| > 2 \Rightarrow x>2, x<-2$
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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 $\displaystyle 0$.
    Surely you mean "x> 0".

    Therefore, the domain of this function is :

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

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