Question

x в степени logx по основанию 3 =9x

Answer 1

$x^{log_3 x}=9x, \ x>0, \ log_3(x^{log_3 x})=log_3(9x), \ log_3 x cdot log_3 x=log_3 9 + log_3 x, \ log_3^ 2 x - log_3 x - 2 = 0, \ log_3 x = t, \ t^2-t-2=0, t_1=-1, t_2=2, \ log_3 x = -1, \ x=3^{-1}, \ x=frac{1}{3}; \ log_3 x = 2 \ x=3^2, \ x=9.$