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Math Help - Re: Big O problem 2

  1. #1
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    Re: Big O problem 2

    I have one more problem. Arrange the functions 2^100n, 2^n^2, 2^n!, 2^2^n, n^logn, nlogn loglogn, n^3/2, n(logn)^3/2, and n^4/3(logn)^2
    in a list so that each function is big-O of the next function. [Hint: To determine the relative size of some of these functions, take logarithms.]

    Some of it I get. One of my main problems is how to do a log of a log. Would you be able to run me through your thought process?
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  2. #2
    MHF Contributor
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    Re: Big O problem 2

    I tried the problem out. 2n!, 2^2^n,2^n^2, 2^100n, n^4/3 (logn)^2, n^3/2, n(logn)^3/2, nlogn loglogn. How far off am I?
    First, the problem says to arrange the functions in increasing, not decreasing, order. Second, it is not clear whether you mean (2^100)n or 2^(100n), 2n! or 2^(n!). The function n^log n = O(2^(100n)) and n^(4/3) (log n)^2 = O(n^log n).
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