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Math Help - For which values of n does equation 2 become smaller than equation 1?

  1. #1
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    For which values of n does equation 2 become smaller than equation 1?

    Please allow me to introduce myself; Name is Morris, I am a computer programmer.

    For which values of n does equation 2 become smaller than equation 1?

    1. 8(n^2)
    2. 64 n (log n to base 2)

    Show clear working please.
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  2. #2
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    Re: For which values of n does equation 2 become smaller than equation 1?

    Quote Originally Posted by mmwanga View Post
    Please allow me to introduce myself; Name is Morris, I am a computer programmer.

    For which values of n does equation 2 become smaller than equation 1?

    1. 8(n^2)
    2. 64 n (log n to base 2)

    Show clear working please.
    1. I assume that you want to solve for n the inequality

    8n^2 < 64 n \log_2(n)

    2. What kind of number is n? Real or natural? I'm going to use real numbers!

    3. It is a little bit easier to solve the equation

    8n^2 = 64 n \log_2(n)

    for n, but I doubt that you can solve this equation algebraically. So use a numerical iterative method.
    With Newton's method you'll get n \approx 1.099997

    4. To answer your question: For n \in (0, 1.099997) the 2nd term is smaller than the 1st one.
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  3. #3
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    Re: For which values of n does equation 2 become smaller than equation 1?

    Thank you for this answer. Would this wolfram alpha plot accurately represent this solution?

    http://www.wolframalpha.com/input/?i=plot+8+x+^+2+%2C+64+x+log+[2%2Cx]%2C+x%3D0+to+2

    In Wolfram alpha : plot 8 x ^ 2 , 64 x log [2,x], x=0 to 2
    Last edited by mmwanga; October 26th 2012 at 12:44 PM.
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  4. #4
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    Re: For which values of n does equation 2 become smaller than equation 1?

    Quote Originally Posted by mmwanga View Post
    Thank you for this answer. Would this wolfram alpha plot accurately represent this solution?

    ...
    1. Yes

    2. I would use a slightly different scaling of the axes such that you can read the coordinates of the point of interception. (see attachment)
    Attached Thumbnails Attached Thumbnails For which values of n does equation 2 become smaller than equation 1?-par_log_interc.png  
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    Re: For which values of n does equation 2 become smaller than equation 1?

    Thank you! Using a different scale definitely makes it more
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    Re: For which values of n does equation 2 become smaller than equation 1?

    sorry about this replay
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