document.write( "Question 1113751: (x^y)=(y^x) ; (x^2)=(y^3)
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Algebra.Com's Answer #728845 by math_helper(2461) $\"\"$ $\"About$

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By inspection, there is a trivial answer x = y = 1.\r
\n" ); document.write( "\n" ); document.write( "But there is also a nontrivial answer.
\n" ); document.write( "ЧЧ\r
\n" ); document.write( "\n" ); document.write( " $\"+x%5E2+=+y%5E3+\"$ Ч>

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\n" ); document.write( "\n" ); document.write( " $\"+x%5Ey+=+y%5Ex+\"$ and the above Ч>

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\n" ); document.write( "\n" ); document.write( "Taking logs:\r
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Ч> $\"+x+=+%283%2F2%29%5E3++=+27%2F8+\"$ Ч> $\"+y+=+9%2F4+\"$
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\n" ); document.write( "\n" ); document.write( " Ans: $\"++highlight%28+x+=+27%2F8+%29+\"$ Ч> $\"+highlight%28++y+=+9%2F4+%29+\"$
\n" ); document.write( "Ч\r
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\n" ); document.write( "Check:
\n" ); document.write( " $\"+x%5E2+=+%2827%2F8%29%5E2+=+729%2F64+\"$
\n" ); document.write( " $\"+y%5E3+=+%289%2F4%29%5E3+=+729%2F64+++\"$ (ok)
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\n" ); document.write( "\n" ); document.write( " $\"+x%5Ey++=++%2827%2F8%29%5E%289%2F4%29+=++%28+3%5E27+%2F+2%5E27+%29+%5E%281%2F4%29++\"$
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(ok)\r
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\n" ); document.write( "\n" ); document.write( "ЧЧЧ
\n" ); document.write( "EDITED: removed statement that x=y=0 is a trivial answer, it is not (0/0 form).
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