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February 22nd, 2017, 11:24 PM   #1
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Year 10 Maths: How many solutions can you find to the equation

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?

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Last edited by skipjack; February 23rd, 2017 at 12:02 PM.
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February 22nd, 2017, 11:52 PM   #2
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Math Focus: Yet to find out.
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.
Thanks from topsquark

Last edited by skipjack; February 23rd, 2017 at 12:02 PM.
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February 23rd, 2017, 02:43 PM   #3
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The problem was previously posted here.
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