2007-12-26 11:28:10 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1.55
ok thanks
2007-12-26 21:45:00 · answer #1 · answered by sanjeewa 4 · 0⤊ 0⤋
As others have mentioned, it is approximately 1.559610469462369, which may be found using numerical methods. If you want a closed-form solution, it can be expressed in terms of the Lambert W function as follows:
x^x = 2
x ln x = ln 2
ln x e^(ln x) = ln 2
ln x = W(ln 2)
x = e^(W(ln 2))
Or, a slight simplification:
x = (W(ln 2) e^(W(ln 2)))/W(ln 2)
x = ln 2 / W(ln 2)
And we are done.
2007-12-26 21:40:11 · answer #2 · answered by Pascal 7 · 0⤊ 0⤋
I found a numerical solution
x = 1.55961
2007-12-26 19:38:39 · answer #3 · answered by Any day 6 · 0⤊ 0⤋
About 1.55961046946237, more or less.
2007-12-26 19:42:35 · answer #4 · answered by morningfoxnorth 6 · 0⤊ 0⤋
1.55...
2007-12-26 19:39:09 · answer #5 · answered by oracle 5 · 0⤊ 0⤋