# Solutions for a^b = b^a?Watch

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#1
Obviously when a=b for any integer.

How can you find out all solutions?

Something to do with logs?
0
14 years ago
#2
(Original post by Widowmaker)
Obviously when a=b for any integer.

How can you find out all solutions?

Something to do with logs?
The only distinct postive integer pair solving this is 2^4=4^2.

More generally, for reals, if you rewrite the equation as

lna/a = lnb/b

and sketch the graph of y = lnx/x you'll see that for every b>1/e there is a unique a in the range 1<a<1/e such that a^b = b^a.
0
14 years ago
#3
http://www.qbyte.org/puzzles/p048s.html
integer sol's is in there
0
14 years ago
#4
(Original post by Widowmaker)
Obviously when a=b for any integer.

How can you find out all solutions?

Something to do with logs?
I had this question for my interview test at Trinity...
0
14 years ago
#5
(Original post by Euler)
I had this question for my interview test at Trinity...

What did you say?
0
14 years ago
#6
(Original post by ~Raphael~)
What did you say?
the only integer solution is 2^4=4^2

said something like take logs, and draw the graph of the result and observe some blah!

it was partially correct...
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