AMC 12 2022a Problem 11

What is the product of all real numbers $x$ such that the distance on the number line between $\log_6x$ and $\log_69$ is twice the distance on the number line between $\log_610$ and $1$?

$\textbf{(A) } 10 \textbf{(B) } 18 \textbf{(C) } 25 \textbf{(D) } 36 \textbf{(E) } 81$