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Determine Big O of a function (Discrete math)

  1. Oct 9, 2013 #1
    Determine whether the function log(n2+1) is O(logn).

    Definition in paint document if needed.


    n2 + 1 < 2n2 whenever n>1

    log(n2 + 1) < log( 2n2 ) = log(2) + 2log(n).

    Now, log(n)>log(2) whenever n>2. Therefore

    log(2) + 2log(n)<3log(n).

    log(n2 + 1) ≤ 3log(n) whenever n>2.
    ∴Because there exists constants C and k such that log(n2 + 1)≤Clog(n) whenever n>k we can conclude log(n2 + 1) is O(logn).

    Is this correct? The book says that log(n2 + 1) is not O(logn).

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  2. jcsd
  3. Oct 9, 2013 #2


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    I think the book is wrong and you are right.
  4. Oct 9, 2013 #3


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    I think you are right and your book is mistaken.
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