Question

Is x^(lny)=y^(lnx) ?

Answer 1

lnx*lny = lnx*lny
ln(y^lnx) = ln(x^lny)
raise both sides with e
e^ln(y^lnx) = e^ln(x^lny)

y^lnx = x^lny

Answer 2

lets take log on both sides
ln y *ln x = ln x * ln y
LHS=RHS
hence proved

Answer 3

Something about this just doesn't seem right even though that's exactly what I did to get this in the first place. Oh well haha thanks.