Prove that a^b = b^a where b,a are not 0/1, has no solns other than 2 & 4?

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Prove that a^b = b^a where b,a are not 0/1, has no solns other than 2 & 4?

2006-09-29 13:46:26 · 2 answers · asked by vnavinv 1 in Science & Mathematics ➔ Mathematics

forgot to mention a not equal to b

2006-09-29 13:47:02 · update #1

integer solns

2006-09-29 13:48:46 · update #2

2 answers

You also forgot to mention that a and b are natural
numbers!
Hint: Take the natural log of both sides and show one
of the variables must be less than e. Use some
elementary calculus!

2006-09-29 13:52:46 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋

Check out my math group:

http://groups.yahoo.com/group/School_Mathematics_Study_Group/

File: The Exponet Problem (Solution)

2006-09-29 16:22:07 · answer #2 · answered by Jerry M 3 · 0⤊ 0⤋