[" If "a,b,c" are all positive and are pth,quth and nth term of a G.P.then sh "],[qquad Delta=|[log a,p,1],[log b,q,1],[log c,r,1]|=0]

If a,b,c are all positive, and are p^(th), q^(th) and r^(th) terms of a G.P., show that |("log"a,p,1),("log"b,q,1),("log"c,r,1)|=0 .

If a,b,are positive and are the pth, qthrth terms respectively of a GP then det[[log a,p,1log b,q,1log c,r,1]]=

If a,b,c are positive and ar the p^(th),q^(th),r^(th) terms respectively of a G.P show that, |{:(,log a,p,1),(,log b,q,1),(,log c,r,1):}|=0

If a , b , c are all positive and are p t h ,q th and r t h terms of a G.P., then '\begin{vmatrix} log a & p & 1 \\ log b & q & 1 \\ log c & r & 1 \\ \end{vmatrix}=0

If a gt 0, b gt 0, c gt0 are respectively the pth, qth, rth terms of a G.P., then the value of the determinant |(log a,p,1),(log b,q,1),(log c,r,1)| , is

If a gt 0, b gt 0, c gt0 are respectively the pth, qth, rth terms of a G.P., then the value of the determinant |(log a,p,1),(log b,q,1),(log c,r,1)| , is

If a,b,c are respectively the pth ,qth and rth terms of a G.P. then (q-r) log a +(r-p) log b+(p-q) log c=

(iii) If a,bc are respectively the pth,qth and rth terms of the given G.P. then show that (q-r)log a+(r-p)log b+(p-q)log c=0, where a,b,c>0.