If `5^x=3^y=45^z,` prove that `1/z=1/x+2/y.`

If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

5^(x)=3^(y)=15^(z), Prove that (1)/(z)=(1)/(x)+(1)/(y)

If 2^(x)=3^(y)=6^(-z) prove that (1)/(x)+(1)/(y)+(1)/(z)=0

If x+y+z=xyz , prove that x/(1-x^2)+ y/(1-y^2)+z/(1-z^2) =(4xyz)/((1-x^2)(1-y^2)(1-z^2))

If 3^(x)=5^(y)=45^(z), then a.(2)/(z)=(1)/(y)-(1)/(x)b(2)/(y)=(1)/(x)-(1)/(z)c*(2)/(x)=(1)/(z)-(1)/(y)dx+y+z=0

If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

If x+y+z=xyz , prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) cdot(3y-y^3)/(1-3y^2)cdot(3z-z^3)/(1-3z^2)

If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove that x y z=-1 .

If x+y+z=xzy , prove that : x(1-y^2) (1-z^2) + y(1-z^2) (1-x^2) + z (1-x^2) (1-y^2) = 4xyz .