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 Needed: a large calculator! (Posted on 2006-09-22)
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: 2.6667 (3 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.

 Subject Author Date re: some thoughts Charlie 2006-09-22 22:25:45 B-A and continued fractions JLo 2006-09-22 18:20:59 some thoughts Dennis 2006-09-22 15:58:04 re: Part 1 spoiler: Be sure the calculator's large enough; soln to part 1 Charlie 2006-09-22 15:44:53 Part 2 spoiler Charlie 2006-09-22 14:26:48 Part 1 spoiler: Be sure the calculator's large enough; soln to part 1 Charlie 2006-09-22 13:43:45

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