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Topic: x^2 = 2^x and x^4 = 4^x
Replies: 5   Last Post: Oct 30, 2013 10:29 PM

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Virgil

Posts: 7,011
Registered: 1/6/11
Re: x^2 = 2^x and x^4 = 4^x
Posted: Oct 30, 2013 4:30 AM
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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.
--





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