If x,y,z , are all positive and are the pth ,qth and rth terms of a geometric progression respectively, then the value of the determinant |logxp1logyq1logzr1| =

If A,R are the first term and common ratio of the G.P then x=ARP−1 ,y=ARq−1 ,z=ARr−1 |logxp1logyq1logzr1|=|log(ARP−1)p1log(ARq−1)q1log(ARr−1)r1|=|logA+(p−1)logRp1logA+(q−1)logRq1logA+(r−1)logRr1|=|(p−1)logRp1(q−1)logRq1(r−1)logRr1|=logR|(p−1)p1(q−1)q1(r−1)r1|=0