How to solve $x\log(x) = 10^6$ I am trying to solve
$$x\log(x) = 10^6$$
but can't find an elegant solution. Any ideas ?

You won't find a "nice" answer, since this is a transcendental equation (no "algebraic" solution).  There is a special function related to this called the Lambert W-function, defined by  $ \ z = W(z) \cdot e^{W(z)} \ $ .  The "exact" answer to your equation is
$ \ x = e^{W( [\ln 10] \cdot 10^6)} \ . $  (I'm assuming you're using the base-10 logarithm here; otherwise you can drop the $ \ln 10 $ factor.)
