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Solving for variable N when it is used as a base and exponent

  1. Sep 25, 2010 #1
    1. The problem statement, all variables and given/known data

    I would like to solve the following equation for the variable "n"
    The variable c represents any integer constant.

    (n/2)^n = c

    The goal is to get this in some form of n = ?

    2. Relevant equations

    The logarithm properties.

    3. The attempt at a solution

    I've tried using logs but I get stuck because there seems to be no way to somehow combine n as a base, and n as an exponent. Is this something that requires higher level math?

    Let all logs be of base 2

    (n/2)^2 = c
    log(n/2)^n = log(c)
    n*log(n/2) = log(c)
    n(log(n)-log(2)) = log(c)
    n(log(n)-1) = log(c)

    Here I get stuck because any further logarithm manipulation only goes in circles.

    Can anyone teach or point to me what kind of math I need to know to solve this please?
  2. jcsd
  3. Sep 25, 2010 #2
    Why didn't you move -log(2) over to the other side? Also, I like natural logs better when you're dealing with variables because you don't have to worry about the base.
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