Question

Найти возможные значения x, если:
2$log_{x}$3=3$log_{3}$x

Answer 1

$2log_{x}3=3log_3x; ,; ; ODZ:; x textgreater 0,; xne 1\\2cdot frac{1}{log_3x}-3log_3x=0\\ frac{2-3log^2_3x}{log_3x} =0; ,; ; to ; ; left { {{2-3log^2_3x=0} atop {log_3xne 0}} right. \\ left { {{log^2_3x=frac{2}{3}} atop {xne 1}} right. ; ; left { {{log_3x=pm sqrt{frac{2}{3}}} atop {xne 1,; x textgreater 0}} right. ; ,; left { {{x=3^{pm sqrt{frac{2}{3}}}} atop {xne 1,x textgreater 0}} right. \\Otvet:; ; x=3^{sqrt{2/3}}; ,; x=3^{-sqrt{2/3}}.$