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Self Power to Googol (Posted on 2023-03-27) Difficulty: 3 of 5
Find x such that

xx = 10100

  Submitted by Charlie    
Rating: 5.0000 (1 votes)
Solution: (Hide)
x=
56.96124843226082030512229823694572038121955668094908795630 ...
88089808892097884521100012184348454866564614437738611477053139

The ... does not indicate any digits are missing but merely ties the two lines together.

is sufficiently accurate to exceed a googol by a tiny fraction of a unit.

digits 5000;
x=vpa(5000);
goal=vpa(10)^100;
lg=vpa(100);
for i=1:50
  x=lg/log10(x)*.8 + x*.2
end

The use of averaging in 20% of the previous value speeds up the convergence.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsa rough approximation using basic principlesbroll2023-03-28 00:18:18
SolutionPuzzle SolutionK Sengupta2023-03-27 22:18:06
SolutionNon-sophisticated numeric approach.Larry2023-03-27 14:11:33
Solutioneasy way / hard wayJer2023-03-27 14:11:25
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