A little help with these would be of help!
i) x^y= y^x
x^2=y^3
Solve for x and y.
ii)a^x=x^y
a^y=x^x
Same here.
Hello Arka
Welcome to Math Help Forum!By inspection, we can see that one solution is . But if , then we can take logs, knowing that :
, provided .
or
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.
Grandad
Hello ArkaYes, you can; although it would have been helpful if you had said so at the beginning.
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,
Grandad