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`

Explanation

We have
|{:(1,,(log y)/(log x),,(log y)/(log x)),((log x)/(logy),,1,,(log z)/(log y)),((log x)/(log y),,(log y)/(log z),,1):}|` (Changing base of logarithm) ltbrtgt Taking `(1)/(log x), (1)/(log y) " and " (1)/(log z) " common from " R_(1) ,R_(2) " and " R_(3)f " respectively we get "`
`Delta= (1)/(" log x log y log z ") |{:(log x,,log y,,log z),(log x,,log y,,log z),(log x,,log y,,log z):}|`
`:. Delta =0 " ""(As "R_(1) ,R_(2) " and "R_(3) " are identical "`