AMC 12 2020a 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 \textbf{(B)}\ 7 \textbf{(C)}\ 10 \textbf{(D)}\ 12 \textbf{(E)}\ 13