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?

(In reply to some thoughts by Dennis)

While it's indeed true that

Log A > 7.964117x10^19*log2 = 2.39744x10^19 (to 5 dec. places)

Log B < 5.024799x10^19*log3 = 2.39744x10^19 (to 5 dec. places)

the numbers approximated (note the power of 10 added, but it's to both so immaterial for this point), are actually, for the numbers given that make them up:

23974381059774389244.82056565
and
23974384035941050952.57618913

so indeed log A can be larger than the former, while log B is smaller than the latter, but log B is still larger than log A, while each number is the same to 7 significant digits.

For part 2, you're interpreting C=2^2^2^83 as (((2^2)^2)^2)^83, rather than as  2^(2^(2^83)). Similarly for D. Federico wouldn't make it so easy.

Posted by Charlie on 2006-09-22 22:25:45