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0.5^n = n
n= ?

2007-05-02 23:01:30 · 1 answers · asked by Anonymous in Science & Mathematics Mathematics

1 answers

You cannot solve that just using logarithms alone. To get a closed-form solution, the Lambert W function (or some equivalent) is required. If you have it, then you can proceed as follows:

(1/2)^n = n

Rewrite this as a power of e:

e^(-n ln 2) = n

Multiply by ln 2 e^(n ln 2):

ln 2 = n ln 2 e^(n ln 2)

Invoke the Lambert W function:

W(ln 2) = n ln 2

Divide by ln 2:

n = W(ln 2)/ln 2

And we are done.

2007-05-02 23:25:06 · answer #1 · answered by Pascal 7 · 1 0

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