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

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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

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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$$=1p$$α$$+(p$$−$$1)$$β$$1q$$α$$+(q$$−$$1)$$β$$1r$$α$$+(r$$ $$1)$$βUsing $$C3$$→$$C3$$−$$($$α−β$$)C1$$−β$$C3$$, we get Δ$$=0$$

Suppose $a, b, c > 0$ and $a, b, c$ c are the $p t h, q t h, r t h$ terms of a G.P. Let $Δ = |\begin{array}{lll} 1 p \log a \\ 1 q \log b \\ 1 r \log c \end{array}|$ then numerical value of $∆$ is

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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

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Suppose $a, b, c > 0$ and $a, b, c$ c are the $p t h, q t h, r t h$ terms of a G.P. Let $Δ = |\begin{array}{lll} 1 p \log a \\ 1 q \log b \\ 1 r \log c \end{array}|$ then numerical value of $∆$ is