Решите log3(x-2)+log3(x+2)=log3(2x-1)

[latex]log_3(x-2)+log_3(x+2)=log_3(2x-1)\ log_3frac{x-2}{x+2}=log_3(2x-1)\ left { {{frac{x-2}{x+2}=2x-1} atop {frac{x-2}{x+2} extgreater 0}; 2x-1 extgreater 0} ight. \ left { {{x-2=(2x-1)(x+2)} atop { left { {{x-2 extgreater 0} atop {x+2 extgreater 0}} ight. }; left { {{x-2 extless 0} atop {x+2 extless 0}} ight. ; x extgreater frac{1}{2}} ight. \ left { {{0=2x^2-x+4x-2-x+2} atop { left { {{x-2 extgreater 0} atop {x+2 extgreater 0}} ight. }; left { {{x-2 extless 0} atop {x+2 extless 0}} ight. ; x extgreater frac{1}{2}} ight. \[/latex][latex] left { {{2x^2+2x=0} atop { left { {{x extgreater 2} atop {x extgreater -2}} ight. }; left { {{x extless 2} atop {x extless -2}} ight. ; x extgreater frac{1}{2}} ight. \ left { {{2x(x+1)=0} atop x extgreater 2ight. \ left { left { {{x=0} atop {x+1=0}} ight. } atop x extgreater 2ight. \ left { left { {{x=0} atop {x=-1}} ight. } atop x extgreater 2ight. \ [/latex]Получаем, что уравнение не имеет решений