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Solve for the nth exponent.

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data
    find n.

    2. Relevant equations
    2^2^n = 36trillion

    3. The attempt at a solution
    I have worked this out and found n to be equal to 3.67 can someone confirm that i have the right solution? I took the log on both sides and worked it out.
  2. jcsd
  3. Feb 24, 2009 #2


    Staff: Mentor

    I get n ~ 5.4929. You have to take the log of both sides twice.
    For my value of n, 2^n ~ 45.03, and 2 to that power is close to 36 trillion.
  4. Feb 24, 2009 #3
    That's correct that 2^n = 36trillion and n=45, i get this also. But when i attempt to get n when 2^2^n = 36 trillion i first convert 2^nlog2 =log(36trillon)
    which becomes log 2^nlog2 =log(log(36 trillion)), now at this point i divide both sides by log2. Now im totally stuck and lost. Can you explain the process?
  5. Feb 24, 2009 #4


    Staff: Mentor

    2^(2^n) = 36 x 10^12
    ==> (2^n) log 2 = log(36 x 10^12)
    ==> n log(2) + log(log 2) = log(log(36 x 10^12))

    Now, subtract log(log 2) from both sides, and then divide both sides by log(2).

    I think you did something weird with the exponents when you got 2^nlog2. The exponent on 2 of your original express is 2^n, so when you take the log of 2^2^n, you get 2^n * log 2, and not what you show.
  6. Feb 24, 2009 #5
    Oh i see, you have to add them and then subtract them then divide by log(2). thanks a lot, you've been very helpfull :).
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