bonanova Posted October 14, 2015 Report Share Posted October 14, 2015 How many solutions exist for xy = yx? xy=yx Quote Link to comment Share on other sites More sharing options...
0 BobbyGo Posted October 14, 2015 Report Share Posted October 14, 2015 Should we assume that x and y are always unique values?If x=y, then there are an infinite number of solutions. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 14, 2015 Author Report Share Posted October 14, 2015 Count your example as one of the "solutions." Quote Link to comment Share on other sites More sharing options...
0 CaptainEd Posted October 15, 2015 Report Share Posted October 15, 2015 how bout...y = log(x)x^log(x) = log(x)^x Quote Link to comment Share on other sites More sharing options...
0 k-man Posted October 15, 2015 Report Share Posted October 15, 2015 ...or more in general...Let y=f(x)Solve f(x)x=xf(x) for x. There are unlimited number of y=f(x) for which a real solution exists for f(x)x=xf(x) For example, let y=2x. Solving (2x)x=x2x results in x=2. Therefore, y=2x=4. 2^4=4^2.Another example is what CaptainEd found above Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted October 15, 2015 Report Share Posted October 15, 2015 As long as y > 0 there always exist a solution. Quote Link to comment Share on other sites More sharing options...
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bonanova
How many solutions exist for xy = yx?xy=yx
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