Virgil
Posts:
8,833
Registered:
1/6/11


Re: x^2 = 2^x and x^4 = 4^x
Posted:
Oct 30, 2013 4:30 AM


In article <Pine.NEB.4.64.1310300053190.25395@panix3.panix.com>, William Elliot <marsh@panix.com> wrote:
> On Mon, 28 Oct 2013, James Ward wrote: > > > The two equations: > > > > x^2 = 2^x and x^4 = 4^x, > > > > both have 3 identical real solutions: > > Of course, they're basically the same equations. > > > x = 2, 4, and infinite power tower of (1/sqrt(2)) > > What's the infinite power tower of (sqr 2)/2?
It is, apparently, approximately 0.766664695962, at least that approximates the other common solution of those two equations. 

