0,} \atop {(x-4)^2>0,}} \right. \\ \left \{ {{x>2,} \atop {x-4\neq0,}} \right. \\ \left \{ {{x>2,} \atop {x\neq4,}} \right. \\ 2log_3(x-2)+2log_3(x-4)=0, \\ log_3(x-2)+log_3(x-4)=0, \\ log_3(x-2)(x-4)=log_31, \\ (x-2)(x-4)=1, \\ x^2+6x+7=0, \\ D_1=3^2-7=2, \\ x_1=-3-\sqrt2<0<2,\\ x_2=-3+\sqrt2<0<2;" alt="2log_3(x-2)+log_3(x-4)^2=0, \\ \left \{ {{x-2>0,} \atop {(x-4)^2>0,}} \right. \\ \left \{ {{x>2,} \atop {x-4\neq0,}} \right. \\ \left \{ {{x>2,} \atop {x\neq4,}} \right. \\ 2log_3(x-2)+2log_3(x-4)=0, \\ log_3(x-2)+log_3(x-4)=0, \\ log_3(x-2)(x-4)=log_31, \\ (x-2)(x-4)=1, \\ x^2+6x+7=0, \\ D_1=3^2-7=2, \\ x_1=-3-\sqrt2<0<2,\\ x_2=-3+\sqrt2<0<2;" align="absmiddle" class="latex-formula">
действительных корней нет.