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Needed: a large calculator! (Posted on 2006-09-22) Difficulty: 3 of 5
Which is greater, A=2^79,641,170,620,168,673,833 or B=3^50,247,984,153,525,417,450?

And what about C=2^2^2^83 and D=3^3^3^52?

  Submitted by Federico Kereki    
Rating: 2.7500 (4 votes)
Solution: (Hide)
Working to 10 digits, both equal approximately 5.0760252191 × 10^23,974,381,246,463,762,439; you need twenty digits' precision to see that B is the greater one. Jlo's continued fractions approach shows how to obtain the exponents in A and B.

As to the second, taking logarithms, and then taking logarithms again, shows that D is bigger.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle ThoughtsK Sengupta2023-02-21 22:17:10
re: some thoughtsCharlie2006-09-22 22:25:45
SolutionB-A and continued fractionsJLo2006-09-22 18:20:59
Some Thoughtssome thoughtsDennis2006-09-22 15:58:04
re: Part 1 spoiler: Be sure the calculator's large enough; soln to part 1Charlie2006-09-22 15:44:53
SolutionPart 2 spoilerCharlie2006-09-22 14:26:48
Part 1 spoiler: Be sure the calculator's large enough; soln to part 1Charlie2006-09-22 13:43:45
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