Logging $x$

$(2x)^x = 216$ $2^x x^x = 2^3 3^3$ $x = \boxed{3}$

$\begin{aligned} \log_{2x} 216 & = x \\ \frac {\log_2 (2^33^3)}{\log_2 (2x)} & = x \\ \frac {3+3\log_2 3}{1+\log_2 x} & = x & \small \color{#3D99F6} \text{Multiplying both sides by }1+\log_2 x \\ {\color{#3D99F6}3} + {\color{#3D99F6}3}\log_2 {\color{#3D99F6}3} & = {\color{#3D99F6}x} + {\color{#3D99F6}x}\log_2 \color{#3D99F6}x & \small \color{#3D99F6} \text{Noting the positions of } x \text{ and 3 on both sides} \\ \implies \color{#3D99F6}{x} & = \boxed{\color{#3D99F6}{3}} \end{aligned}$