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Solve expression for k

  1. Oct 10, 2008 #1
    I would like to solve [tex] 2^k = \frac{n}{k} [/tex] for k in terms of n, but can't seem to do it. Any help greatly appreciated!
     
  2. jcsd
  3. Oct 10, 2008 #2

    Defennder

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    Hm, there may not be a closed form solution. Does anyone else have better luck?
     
  4. Oct 11, 2008 #3

    Dick

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    No, you can't solve it algebraically. You can only approximate it numerically, unless n is very special.
     
    Last edited: Oct 11, 2008
  5. Oct 11, 2008 #4
    Thanks, thats what I wanted to know. Cheers
     
  6. Oct 12, 2008 #5

    HallsofIvy

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    That depends upon what you mean by "closed form" or "algebraic" solution.

    This is obviously equivalent to k2k= n and, since 2k= ekln(2), k ek ln(2)= n. Multiplying on both sides by ln 2, (k ln(2)) ek ln(2)= n ln(2). If we let y= k ln(2), that equation is yey= n ln(2).

    That equation is directly solvable by the Lambert W function (which is simply defined as the inverse function to f(x)= xex): k ln(2)= y= W(n ln(2)) so
    k= W(n ln(2))/ln(2).
     
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