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Problem from Amc involving logs

  1. Sep 1, 2012 #1
    The Following is defined,

    log2004(log2003(log2002(log2001x)))

    where x > c, what is c?

    Answer is 2001^2002, but how to obtain it?

    I do not know much about logs as I am only in precalculus.
     
  2. jcsd
  3. Sep 1, 2012 #2

    Remember that (the real) logarithm function at any base is defined only on the real positive numbers, thus it must be
    $$\log_{2003}(\log_{2002}(\log_{2001}(x)))>0$$
    (I'm assuming that those numbers you wrote in such an unclear way are the logarithms' bases), and from here
    $$\log_{2002}(\log_{2001}(x))>1\Longrightarrow \log_{2001}(x)>2002\Longrightarrow...etc $$

    DonAntonio
     
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