2020 AMC 12A Problem 17

The vertices of a quadrilateral lie on the graph of $y = \ln x$ , and the $x$ -coordinates of these vertices are consecutive positive integers. The area of the quadrilateral is $\ln \frac{91}{90}$ . What is the $x$ -coordinate of the leftmost vertex?

$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 7\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 13$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.