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. " alt="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. " align="absmiddle" class="latex-formula">