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Thread: log problem

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    19

    log problem

    The tower function of twos is defined recursively as follows: $\displaystyle T(1) = 2$ and $\displaystyle T(n+1) = 2^{T(n)}$ for $\displaystyle n\geq1$. Let $\displaystyle A = (T(2009))^{T(2009)}$ and $\displaystyle B = (T(2009))^A$. What is the largest integer $\displaystyle k$ such that

    $\displaystyle \underbrace{\log_{2}\log_{2}\log_{2}...\log_{2}} B $
    $\displaystyle k$ times

    is defined?
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  2. #2
    Junior Member
    Joined
    Sep 2008
    Posts
    31
    Wasn't this a problem on the AMC 12A this year?
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