Suppose a,b,c>0 and a,b,c c are the pth, qth, rth terms of a G.P. Let Δ=1    p    log⁡a1    q    log⁡b1    r    log⁡c then numerical value of ∆ is

Let a=ARp−1,b=ARq−1and c=ARr−1⇒log⁡a=α+(p−1)β,log⁡b=α+(q−1)β andlog⁡c=α+(r−1)βwhere        α=log⁡a,β=log⁡RNow,           Δ=1pα+(p−1)β1qα+(q−1)β1rα+(r 1)βUsing C3→C3−(α−β)C1−βC3, we get Δ=0