AMC 12 2024b 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 $\triangle ABC$?

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