If `x^[ln[y/z]].y^[ln[xz]^2].z^[ln[x/y]]=y^[4lny]` for any x>1,y>1 and z>1, then which one of the following is correct?

Given that log_(x)y,log_(z)x,log_(y)z are in GP, xyz=64" and "x^(3),y^(3),z^(3) are in A.P. Which one of the following is correct ? x,y and z are

If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

If 2log(x-z)-log(x-2y+z)=log(x+z), then x,y and z are in

If x, y, z be three consecutive intergers, then prove that log(1+xz) = 2 log y

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