Log4x+log4(x-6)=2 надооооооо

Решите задачу:

$log_4x+log_4(x-6)=2\; ,\; \; \; ODZ:\; \; \left \{ {{x\ \textgreater \ 0} \atop {x-6\ \textgreater \ 0}} \right. \; \left \{ {{x\ \textgreater \ 0} \atop {x\ \textgreater \ 6}} \right. \; \to \; x\ \textgreater \ 6\\\\log_x\, x(x-6)=log_42^4\\\\x^2-6x=16\\\\x^2-6x-16=0\; ,\; \; x_1=-2\; ,\; \; x_2=8\; \; (teorema\; Vieta)\\\\x_1=-2\notin ODZ\\\\Otvet:\; \; x=8\; .$