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Homework Help: Determine which is bigger

  1. Feb 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Which is bigger 2^500 or 5^200

    2. Relevant equations

    3. The attempt at a solution
    Well I got to 2^2^250 -> 4^250 vs 5^200... by the looking at it 4^250 is bigger but I can't just say it looks bigger... There are lots of these that I can't get on a common base, so if anyone can point me to the right direction I'll give lots of love.
  2. jcsd
  3. Feb 17, 2010 #2
    divide the two numbers.
    come to a form of (a/b^n)^k * a^k = (a*(a/b^n))^k
    prove that a/b^n > 1/a
    from that you can easily proove that the numerator is bigger than the denominator
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