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−coordinate of the leftmost vertex


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

$T h e v e r t i c e s o f q u a d r i l a t e r a l$ $l i e o n t h e g r a p h o f y = l n x a n d$ $t h e x - c o o r d i n a t e s o f t h e s e v e r t i c e s$ $a r e c o n s e c u t i v e p o s i t i v e i n t e g e r$ $. T h e a r e a o f t h e q u a d r i l a t e r a l$ $i s l n (\frac{91}{90}) . w h a t i s t h e x - c o o r d i n a t e$ $o f t h e l e f t m o s t v e r t e x$
Commented by john santu last updated on 15/Feb/20

$12 ?$
Commented by jagoll last updated on 15/Feb/20

$s o l u t i o n p l s$
Commented by mr W last updated on 15/Feb/20

$A = - \ln n + \ln (n + 1) + \ln (n + 2) - \ln (n + 3)$ $A = \ln \frac{(n + 1) (n + 2)}{n (n + 3)} = \ln \frac{91}{90}$ $\Rightarrow n^{2} + 3 n - 180 = 0$ $\Rightarrow (n + 15) (n - 12) = 0$ $\Rightarrow n = 12$
Commented by jagoll last updated on 15/Feb/20

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