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Math Help - log problem

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    19

    log problem

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

    \underbrace{\log_{2}\log_{2}\log_{2}...\log_{2}} B
    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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