Найти возможные значения x, если: 23=3x

Решите задачу:

$2log_{x}3=3log_3x\; ,\; \; ODZ:\; x\ \textgreater \ 0,\; x\ne 1\\\\2\cdot \frac{1}{log_3x}-3log_3x=0\\\\ \frac{2-3log^2_3x}{log_3x} =0\; ,\; \; \to \; \; \left \{ {{2-3log^2_3x=0} \atop {log_3x\ne 0}} \right. \\\\ \left \{ {{log^2_3x=\frac{2}{3}} \atop {x\ne 1}} \right. \; \; \left \{ {{log_3x=\pm \sqrt{\frac{2}{3}}} \atop {x\ne 1,\; x\ \textgreater \ 0}} \right. \; ,\; \left \{ {{x=3^{\pm \sqrt{\frac{2}{3}}}} \atop {x\ne 1,x\ \textgreater \ 0}} \right. \\\\Otvet:\; \; x=3^{\sqrt{2/3}}\; ,\; x=3^{-\sqrt{2/3}}.$