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kylekatarn
2005-11-02 10:12:54

It's not a proof, but a start.

mathsyperson
2005-11-02 09:23:01

Hmm. It's obvious that once it gets to 2 then it will stay there because (√2)² = 2, but that's not anywhere close to a proof.

kylekatarn
2005-11-02 09:13:16

yes, its very interesting.
As you add up more "^x" terms, the solution get closer to SQRT(2).

Again, I would like to see a demonstration of this (or a counter example)
: )

MathsIsFun
2005-11-02 07:32:21

Well then, you should exponentiate in this order I believe:

x^(x^(x^(x^x)))

In Excel (by trial and error) I get: 1.432694...

Makonorth
2005-11-02 05:26:31

That's exactly how it was written.

kylekatarn
2005-11-02 04:58:35

x^x^x^x^x=2

x ≈ 1.425385621 ≈ √2

I think the solution of x^x^x^...........=2 converges into √2.
If someone proved that it would be remarkable.

mathsyperson
2005-11-02 03:29:15

Is that (((x^x)^x)^x)^x or x^(x^(x^(x^x)))?

I'm just asking that to stall for time, because I have no idea how to start trying to solve it. Probably using logs.

Makonorth
2005-11-01 15:16:37

Someone showed me this problem today and I couldn't think of how to solve it:

x^x^x^x^x = 2

Anyone know how to solve it and if so can you explain how you get to your answer?