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Math Help - Binary Integer Proof?

  1. #1
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    Binary Integer Proof?

    Hi all, any ideas with the following?

    Let n be a positive integer:

    Show that when n is written in binary notation, then the number k of its digits
    satis es

    k - 1 <= ln(n)/ln(2) < k

    where ln is the natural logarithm.

    Thanks!
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  2. #2
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    Quote Originally Posted by sirellwood View Post
    Hi all, any ideas with the following?

    Let n be a positive integer:

    Show that when n is written in binary notation, then the number k of its digits
    satises

    k - 1 <= ln(n)/ln(2) < k

    where ln is the natural logarithm.

    Thanks!


    Let k the positive integer s.t. 2^{k-1}<= n < 2^k . Now apply log basis 2 in the three sides and get what you want

    Tonio
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  3. #3
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    So could I use the same theory for when n is written in decimal notation, then the number L of its digits
    satis fies:

    L-1 <= ln(n)/ln(10) < L?
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