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Math Help - Indices

  1. #1
    Junior Member
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    Indices

    HI. I am having trouble with this question.

    Find the smallest positive integers m and n for which:

    a) 12< 2^{m/n}< 13

    b) 13< 2^{m/n}< 14

    Thanks
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  2. #2
    Member Awsom Guy's Avatar
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    Quote Originally Posted by deltaxray View Post
    HI. I am having trouble with this question.

    Find the smallest positive integers m and n for which:

    a) 12< 2^{m/n}< 13

    b) 13< 2^{m/n}< 14

    Thanks
    a) 2^11/2

    b) 2^15/4
    I hope that helps.
    Last edited by Awsom Guy; November 9th 2009 at 01:01 AM. Reason: My math programing isnt good..
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  3. #3
    Super Member Bacterius's Avatar
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    @Awsom Guy :

    2^{\frac{ 11}{2}} = 2^{5.5} \approx 45

    The second one seems right though. Anyway, a more "algebraic" answer :

    12 < 2^{m/n} < 13

    log_2(12) < log_2(2^{m/n}) < log_2(13)

    log_2(12) < m/n < log_2(13)

    Might make it a bit easier ? (same thing for the other one)
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