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February 22nd, 2017, 10:24 PM  #1 
Member Joined: May 2015 From: Australia Posts: 77 Thanks: 7  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? Thanks. Last edited by skipjack; February 23rd, 2017 at 11:02 AM. 
February 22nd, 2017, 10:52 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,610 Thanks: 550 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. Last edited by skipjack; February 23rd, 2017 at 11:02 AM. 

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