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Math Help - Log-scale

  1. #1
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    Log-scale

    Greetings.

    I seek advise on a question of a general nature. The lack of a specific forum for general issues, I am using this chat room for the same.

    It my readings of technical papers - primarily related to networks & protocols - I encountered the usage of 'log-scale'. It appears that representing certain functions in log-scale accentuates certain properties of the phenomenon the function is representing.

    Would appreciate if someone could corroborate my understanding and shed some more light on the usage of the subject.

    Look forward to a prompt response.

    Best regards,
    wirefree
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by wirefree View Post
    Greetings.

    I seek advise on a question of a general nature. The lack of a specific forum for general issues, I am using this chat room for the same.

    It my readings of technical papers - primarily related to networks & protocols - I encountered the usage of 'log-scale'. It appears that representing certain functions in log-scale accentuates certain properties of the phenomenon the function is representing.

    Would appreciate if someone could corroborate my understanding and shed some more light on the usage of the subject.

    Look forward to a prompt response.

    Best regards,
    wirefree
    I believe a good example would be the factorial function. n! \sim n^ne^{-n}\sqrt{2 \pi m}. This is often shortened and written ln(n!) \sim n ln(n)-n (the \sqrt{2 \pi m} term is only needed for small values of n).

    I don't know if that is precisely what you are looking for. It is quite a neat formula. I came across it being used once in a proof looking at random paths where the terms all canceled neatly. However, if you had just been using n! as opposed to n! \sim n^ne^{-n}\sqrt{2 \pi m} there is no way you would have seen the cancellations!

    I can't quite remember what the book is - it's on my desk, but regrettably my desk is not here!

    EDIT: Meant to say, I'm not actually sure if this is an example or not. I just think it is pretty, and that it is a good example of approximating a function to get much more information about it.
    Last edited by Swlabr; December 15th 2009 at 02:17 AM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by wirefree View Post
    Greetings.

    I seek advise on a question of a general nature. The lack of a specific forum for general issues, I am using this chat room for the same.

    It my readings of technical papers - primarily related to networks & protocols - I encountered the usage of 'log-scale'. It appears that representing certain functions in log-scale accentuates certain properties of the phenomenon the function is representing.

    Would appreciate if someone could corroborate my understanding and shed some more light on the usage of the subject.

    Look forward to a prompt response.

    Best regards,
    wirefree
    Log scales compress the dynamic range of the data making features that would otherwise be invisible visible. Also log-linear and log-log plots render certain types of plot linear.

    CB
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  4. #4
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    Appreciate the response, CaptainBlack.

    Quote Originally Posted by CaptainBlack View Post
    Log scales compress the dynamic range of the data making features that would otherwise be invisible visible.CB
    Could you elaborate on what "invisibilities" might I be dealing with for any given situation?


    Also log-linear and log-log plots render certain types of plot linear.
    Could you please explain why I would be required to render a plot linear?

    Would appreciate a couple of lines of insights.

    Best regards,
    wirefree
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by wirefree View Post
    Appreciate the response, CaptainBlack.



    Could you elaborate on what "invisibilities" might I be dealing with for any given situation?

    f(x)=\begin{cases}0.1\times \sin(x)+0.2, & x <1\\100 \times \cos(20x)+110, & x\ge 1 \end{cases}

    Could you please explain why I would be required to render a plot linear?
    To demonstrate a power law relation.

    CB
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  6. #6
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    Quote Originally Posted by CaptainBlack View Post
    f(x)=\begin{cases}0.1\times \sin(x)+0.2, & x <1\\100 \times \cos(20x)+110, & x\ge 1 \end{cases}
    Following is a plot of the above given piece-wise function. I seek assistance with proceeding with obtaining the log-scale version of the same so as to arrive at an understanding of the relevance of the subject.



    Look forward to a prompt response.

    Best regards,
    wirefree
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