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Math Help - logarithmic function

  1. #1
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    logarithmic function

    Hello, I have the following function:

    h(x) - lnx + ln(2-x)

    The domain of this function is (0,2).
    I understand the rule is that you must find a value of x that results in a sum greater than 0.
    However I cannot understand why the domain could not be (negative infinity, 2).

    For instance if x was -2, then I would have "...ln(2 - - 2)" equalling 4 ?

    Thank you for any insight.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by fran1942 View Post
    Hello, I have the following function:

    h(x) - lnx + ln(2-x)

    The domain of this function is (0,2).
    I understand the rule is that you must find a value of x that results in a sum greater than 0.
    However I cannot understand why the domain could not be (negative infinity, 2).

    For instance if x was -2, then I would have "...ln(2 - - 2)" equalling 4 ?

    Thank you for any insight.
    Don't forget the other part of your function. At x = -2:
    h(-2) = ln(-2) + ln(2 - -2)

    ln(-2) does not exist.

    -Dan
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  3. #3
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    Is this supposed to be \displaystyle h(x) = \ln{(x)} + \ln{(2-x)}?
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  4. #4
    Junior Member mathfun's Avatar
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    lnx exists only when x>0
    ln(2-x) exists only when 2-x>0 or x<2
    So the domain of the function is A=(0,2)
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