" Prove that "x^((log y-log z))y^((log z-log x))z^((log x-log y))=1

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

Prove that x^(log y - logz) xx y^(log z - logx) xx z^(log x - log y) = 1 .

The value of (yz)^(log y-log z)xx(zx)^(log z-log x)xx(xy)^(log x-log y) is

Find the value of (yz)^(log y - log z) xx (zx)^(log z - log x) xx (xy)^(log x - log y) .

Suppose x;y;zgt0 and are not equal to 1 and log x+log y+log z=0 . Find the value of x^(1/log y+1/log z)xx y^(1/log z+1/log x)xx z^(1/logx+1/logy) (base 10)

Using properties of determinant show that |(1,log_x y,log_x z),(log_y x,1,log_y z),(log_z x,log_z y,1)|=0

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)]

Prove that : (iii) (yz)^(log(y/z))(zx)^(log(z/x))(xy)^(log(x/y)) = 1