2024 AMC 12B Problem 15

A triangle in the coordinate plane has vertices A(\log_21,\log_22), B(\log_23,\log_24), and C(\log_27,\log_28). What is the area of \triangle ABC?

\textbf{(A) }\log_2\frac{\sqrt3}7\qquad \textbf{(B) }\log_2\frac3{\sqrt7}\qquad \textbf{(C) }\log_2\frac7{\sqrt3}\qquad \textbf{(D) }\log_2\frac{11}{\sqrt7}\qquad \textbf{(E) }\log_2\frac{11}{\sqrt3}\qquad

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