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?

I thought I had a solution until I read Charlie's response. Now I'm not sure.

A>2^(7.964117x10^19) and B< 3^(5.024799x10^19).

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

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

So log A > log B forcing A > B.

Part 2: C=2^332 and D=3^468. Since log C =332*log2<100 and log D = 468*log3 > 223, log C < log D so C < D.

Posted by Dennis on 2006-09-22 15:58:04