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#2 2005-11-02 03:29:15
- mathsyperson
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Re: Difficult Exponent Problem
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.
Why did the vector cross the road?
It wanted to be normal.
#3 2005-11-02 04:58:35
- kylekatarn
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Re: Difficult Exponent Problem
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.
#5 2005-11-02 07:32:21
- MathsIsFun
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Re: Difficult Exponent Problem
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...
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#6 2005-11-02 09:13:16
- kylekatarn
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Re: Difficult Exponent Problem
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)
: )
#7 2005-11-02 09:23:01
- mathsyperson
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Re: Difficult Exponent Problem
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.
Why did the vector cross the road?
It wanted to be normal.