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Naturally Logarithmic Quadrilateral

Source: 2020 AMC 12A #17

January 31, 2020
2020 AMC 12A2020 AMCquadrilateralcoordinateAMC 12AMC

Problem Statement

The vertices of a quadrilateral lie on the graph of y=ln⁡xy = \ln x, and the xx-coordinates of these vertices are consecutive positive integers. The area of the quadrilateral is ln⁡9190\ln \frac{91}{90}. What is the xx-coordinate of the leftmost vertex?
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 13<span class='latex-bold'>(A)</span>\ 6\qquad<span class='latex-bold'>(B)</span>\ 7\qquad<span class='latex-bold'>(C)</span>\ 10\qquad<span class='latex-bold'>(D)</span>\ 12\qquad<span class='latex-bold'>(E)</span>\ 13
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