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|[log(x)xyz,log(x)y,log(x)z],[log(y)xyz,...

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

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

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

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

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

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

Find the value of |(1,log_(x) y,log_(x) z),(log_(y) x,1,log_(y) z),(log_(z) x,log_(z) y,1)| if x,y,z ne 1

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]]