If `(xy log(xy))/(x+y) = (yz log (yz))/(y+z) = (zxlog (zx))/(z+x)`, then show that `x^(x) = y^(y) =z^(z)`

If (log x)/(y-z)=(log y)/(z-x)=(log z)/(x-y), then prove that: x^(x)y^(y)z^(z)=1

If (log x)/(y-z)=(log y)/(z-x)=(log z)/(x-y) then prove that x^(y)+z^(z)+xx^(y+z)+y^(x+x)+z^(x+y)>=3

If (log_(e)a)/(y-z)=(log_(e)b)/(z-x)=(log_(e)c)/(x-y), then a^(y^(2)+yz)=*b^(z^(2)+zx+x^(2))*c^(x^(2)+xy+y^(2)) equals

Simplify- (x-y)/(xy)+(y-z)/(yz)+(z-x)/(zx)

If xy + yz + zx = 1 find (x+y)/(1-xy) + (y+z)/(1-yz) + (z + x)/(1-zx) = ?

If a = 1 + "log"_(x) yz, b = 1 + "log"_(y) zx, c =1 + "log"_(z) xy, then ab+bc+ca =