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Homework on exponents

  1. Jul 11, 2008 #1
    1. The problem statement, all variables and given/known data


    Hey guys, im having difficulty with the following problem:

    "If m and n are two postive integers, prove that one of m^(1/n) or n^(1/m) is always less than or equal to 3^(1/3)"

    Any idea of how to go about this?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 11, 2008 #2
    Re: Exponents!

    Hmm...

    Well here is what could happen:

    m=n
    m>n or
    m<n

    The last two cases can be treated as one.

    One more hint: for what value of x is [tex]x^{\frac{1}{x}}[/tex] maximized? I think it's e.
     
  4. Jul 11, 2008 #3
    Re: Exponents!

    I don't see how e can be useful since [tex]3^{1/3} \leq e [/tex]
     
  5. Jul 11, 2008 #4
    Re: Exponents!

    If you know where the max value is you should be able to locate the max value for the function on the positive integers by looking at where the function is increasing and decreasing.

    Then deal with the case where m != n
     
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