If `(log_e x)/(y-z)=(log_e y)/(z-x)=(log_e z)/(x-y),` prove that `xyz=1.`

If (log x)/(y-z) = (log y)/(z-x) = (log z)/(x-y) , then prove that xyz = 1 .

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"x)/(y - z) = ("log" y)/(z - x) = ("log" z)/(x - y) , then prove that xyz = 1.

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

If ("log"_(e)x)/(b - c) = ("log"_(e) y)/(c - a) = ("log"_(e) z)/(a - b) , show that xyz = 1

If ("log"_(e)x)/(b - c) = ("log"_(e) y)/(c - a) = ("log"_(e) z)/(a - b) , show that x^(a)y^(b)z^(c ) = 1

(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 (y+z-x)/(log x)=y(z+x-y)/(log y)=z(x+y-z)/(log z) Prove that x^(y)y^(x)=z^(y)y^(z)=x^(z)z^(x)

If x=(log)_(2a)a , y=(log)_(3a)2a ,z=(log)_(4a)3a ,prove that 1+x y z=2y z