Find value of `log_x y * log_y z * log_z x`

Find the value of (x^(log y - log z))(y^(log z-log x))(z^(log x - log y))

Suppose x,y,z>1 then least value of log(xyz)[(log x)/(log y log z)+(log y)/(log x log z)+(log z)/(log x log y)]

If x , y and z be greater than 1, then the value of |{:(1, log_(x)y, log_(x) z),(log_(y)x , 1 ,log_(y)z),(log_(z)x , log_z y , 1 ):}| =