If-loga-and-logb-are-the-roots-of-the-equation-mx-2-nx-s-0-fimd-in-terms-of-m-n-and-s-the-value-of-logab-

Question Number 149208 by pete last updated on 03/Aug/21

$$\mathrm{If}\:\mathrm{loga}\:\mathrm{and}\:\mathrm{logb}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{mx}^{\mathrm{2}} +\mathrm{nx}+\mathrm{s}=\mathrm{0},\:\mathrm{fimd}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{m},\:\mathrm{n}\:\mathrm{and} \\ $$$$\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{logab}. \\ $$

Answered by gsk2684 last updated on 03/Aug/21

$$\mathrm{log}\:{a}\:+\mathrm{log}\:{b}\:=−\frac{{n}}{{m}} \\ $$$$\mathrm{log}\:\left({ab}\right)\:=−\frac{{n}}{{m}} \\ $$

Commented by pete last updated on 03/Aug/21

$$\mathrm{Thanks}\:\mathrm{for}\:\mathrm{yoir}\:\mathrm{time},\:\mathrm{Sir}. \\ $$

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