The-vertices-of-quadrilateral-lie-on-the-graph-of-y-lnx-and-the-x-coordinates-of-these-vertices-are-consecutive-positive-integer-The-area-of-the-quadrilateral-is-ln-91-90-what-is-the-x-c

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Question Number 81734 by jagoll last updated on 15/Feb/20

$$Theverticesofquadrilateral$$$$lieonthegraphofy=lnxand$$$$thex-coordinatesofthesevertices$$$$areconsecutivepositiveinteger$$$$.Theareaofthequadrilateral$$$$isln\left(\frac{91}{90}\right).whatisthex-coordinate$$$$oftheleftmostvertex$$

Commented by john santu last updated on 15/Feb/20

$$12?$$

Commented by jagoll last updated on 15/Feb/20

$$solutionpls$$

Commented by mr W last updated on 15/Feb/20

$$A=-\ln n+\ln (n+1)+\ln (n+2)-\ln (n+3)$$$$A=\ln \frac{(n+1)(n+2)}{n(n+3)}=\ln \frac{91}{90}$$$$\Rightarrow n^2+3n-180=0$$$$\Rightarrow (n+15)(n-12)=0$$$$\Rightarrow n=12$$

Commented by jagoll last updated on 15/Feb/20

$$thankyousir$$

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