[" Show that "],[qquad [1,log_(x)y,log_(x)x],[log_(y)x,1],[log_(x)x,log_(x)x]|=0],[qquad [log_(y)x],[x]|]

1+log_(x)y=log_(2)y

|(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,log_(z)y,1)|=

Prove that , |[1,log_x^y,log_x^z],[log_y^x,1,log_y^z],[log_z^x,log_z^y,1]|=0

The value of |(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,lo_(z)y,1)|=

det[[log_(x)xyz,log_(x)y,log_(x)zlog_(y)xyz,1,log_(y)zlog_(z)xyz,log_(z)y,1]]=0

For positive numbers x,y and z, the numerical value of the determinant det[[log_(x)y,log_(x)zlog_(y)x,1,log_(y)zlog_(z)x,log_(z)y,1]]

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)| is

for x,x,z gt 0 Prove that |{:(1,,log_(x)y,,log_(x)z),(log_(y)x,,1,,log_(y)z),(log_(z) x,,log_(z)y,,1):}| =0

for x,x,z gt 0 Prove that |{:(1,,log_(x)y,,log_(x)z),(log_(y)x,,1,,log_(y)z),(log_(z) x,,log_(z)y,,1):}| =0

for x,x,z gt 0 Prove that |{:(1,,log_(x)y,,log_(x)z),(log_(y)x,,1,,log_(y)z),(log_(z) x,,log_(z)y,,1):}| =0