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B Logarithmic function

  1. Nov 7, 2016 #1
    can domain of logarithm function be R .
    i think it can and the same time it can't
    it can like log(x2)
    but at the same time i think all the logarithm function should be one to one function
     
  2. jcsd
  3. Nov 7, 2016 #2
    and what about the range of logarithmic function can it be other than R
     
  4. Nov 7, 2016 #3

    jedishrfu

    Staff: Mentor

    Here's the wikipedia discussion on logarithms with a chart of the function:

    https://en.wikipedia.org/wiki/Logarithm

    from it you can see that 0 is not a member and that its true for all ##x>0## ie there are no negative values for x.

    Also ##log(x^2)## is equivalent to ##2*log(x)## which gets you back to understanding the domain and range of ##log(x)##
     
  5. Nov 7, 2016 #4
    OK how about log(x2+9)
     
  6. Nov 7, 2016 #5
    does logarithmic always have asymptotes
     
  7. Nov 7, 2016 #6
    i know about logarithmic function but i want to increase my knowledge .
     
  8. Nov 7, 2016 #7

    Mark44

    Staff: Mentor

    No, not true. The domain of ##\log(x^2)## includes the negative reals as well as the positive reals.
    If n is an odd integer, the property ##\log(x^n) = n\log(x)## is applicable only for x > 0. If n is an even integer, then the only restriction on (real) x is that ##x \ne 0##.

     
    Last edited: Nov 7, 2016
  9. Nov 7, 2016 #8

    Mark44

    Staff: Mentor

    Since ##x^2 + 9## > 0 for all real x, the domain of this function is ##\mathbb{R}##.

    The function above doesn't have an asymptote.
     
  10. Nov 7, 2016 #9

    Mark44

    Staff: Mentor

    Based on my other replies, what do you think?
     
  11. Nov 7, 2016 #10

    jedishrfu

    Staff: Mentor

    Yes, you are right.
     
  12. Nov 7, 2016 #11

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    For clarification: The maximal (real) domain is ##\mathbb{R}##. You can define the function on all real numbers, but you don't have to.
     
  13. Nov 7, 2016 #12
    so it can be ℝ
     
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