| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1891.1 | can't do | HERON::BLOMBERG | Trapped inside the universe | Fri Sep 02 1994 06:39 | 7 |
|
It would be equivalent to finding inverse(s) to ln(x)/x which
I don't think you can in a closed form. Relates slightly to
the problem of determining which number is the larger of e^pi and pi^e.
/Ake
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| 1891.2 | probably one answer | AD::GRUNDMANN | Bill | Fri Sep 02 1994 08:44 | 12 |
| How about this (haven't done much math in years)
x^n = n^x
ln(x^n) = ln(n^x)
n * ln(x) = x * ln(n)
n/ln(n) = x/ln(x)
define f(n) = n/ln(n)
we want to find two values where f(n1) = f(n2)
If f(n) is monotonic, you can't do it. I think
f(n) is monotonic, but how do you prove that?
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| 1891.3 | | AMCFAC::RABAHY | dtn 471-5160, outside 1-810-347-5160 | Fri Sep 02 1994 11:08 | 1 |
| (2,4), (4,2), (-2,-4) and (-4,-2)
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| 1891.4 | | CSOA1::LENNIG | Dave (N8JCX), MIG, @CYO | Fri Sep 02 1994 11:35 | 18 |
| I'm not sure what .3 is indicating...
I also took things as far as ln(n)/n = ln(x)/x
Interestingly, the _behaviour_ of ln(n)/n is sort of the same as the
behaviour of the results I determined experimentally
The crossover points (X values) for various N
N ln(n)/n
2 2 4 .151
3 2.4 3 .159
4 2 4 .151
5 1.7 5 .140
6 1.6 6 .130
I'm not sure what to make of the fact N=X isn't always the upper one.
Dave
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| 1891.5 | | AMCFAC::RABAHY | dtn 471-5160, outside 1-810-347-5160 | Fri Sep 02 1994 11:57 | 2 |
| .3 indicates some points that satisfy x**y = y**x other than the
obvious x = y, (where x <> 0)
|
| 1891.6 | | AMCFAC::RABAHY | dtn 471-5160, outside 1-810-347-5160 | Fri Sep 02 1994 12:06 | 3 |
| re .4:
Naturally, the crossover point is e.
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| 1891.7 | topic pointer chain | AUSSIE::GARSON | achtentachtig kacheltjes | Mon Sep 05 1994 00:42 | 3 |
| re .*
-> 1623 -> 512 (where it is analysed in depth)
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| 1891.8 | | CSOA1::LENNIG | Dave (N8JCX), MIG, @CYO | Tue Sep 06 1994 14:25 | 5 |
| Sorry - My DIR/TIT's didn't turn them up.
And thanks - now I have to think about 512 some...
Dave
|