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Exponential Difficulties (Posted on 2004-10-30) Difficulty: 4 of 5
R = N ^ (N ^ (N ^ ...)). What is the maximum N>0 that will yield a finite R?

No Solution Yet Submitted by SilverKnight    
Rating: 3.0000 (1 votes)

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Solution? | Comment 1 of 6

This seems too easy: log(x^a)=alog(x), so log(R)=Rlog(R) and hence R=1 is the only value that works. Thus it looks like N=1 is the only value that works.

The above isn't right. log(R)=Rlog(N).  See next comment by David Shin for the correct analysis.

Edited on October 30, 2004, 6:08 pm
  Posted by Richard on 2004-10-30 17:27:09

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