A little help with these would be of help!
i) x^y= y^x
Solve for x and y.
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, provided .
clearly gives us problems with . So we're left with the solution .
I haven't looked at (ii). I think you could begin in a similar way.
I prefer to use logs, because it avoids handling fractional exponents, but here goes:
Substitute into the equation :
If we now compare the exponents on each side of the equation, we get:
Cube both sides:
Then, as before,