Year 10 Maths: How many solutions can you find to the equation

May 2015
78
7
Australia
How many solutions can you find to the equation:

x^y=y^x (x does not equal y)

The answer is: one, 2^4 = 4^2

I couldn't figure this one out. After looking at the solution, the only way I can think of is through trial and error, even though it might take a long time to get the right answer.

Is there another way to get the answer?

Thanks.
 
Last edited by a moderator:
Feb 2016
1,849
657
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Some more info on it here. Check the links in the top answer.

EDIT: To answer your question, there are other ways (see links), but I'm not sure whether those methods are taught at year 10 level.
 
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