If `x(y+z-x)/logx=y(z+x-y)/logy=z(x+y-z)/logz`; Prove that `x^y y^x=z^y y^z = x^z z^x`

(If(y+z-x))/((x(y+z-x))/(log y))=(y(z+x-y))/(log y)(z(x+y-z))/(log z), prove that x^(y)y^(x)=z^(x)y^(z)=x^(z)z^(x)

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 x + y = 2z then (x)/(x-z) +(z)/(y-z) = ?

If x=y^(z), y = z^(x) and z=x^(y) , then

If x=y^z,y=z^x,z=x^y then

If log x log y log z=(y-z)(z-x)(x-y) then a )x^(y)*y^(z)*z^(x)=1 b) x^(2)y^(2)z^(2)=1c)root(z)(x)*root(y)(y)*root(z)(z)1=d) None of these