Решите логарифмическое уравнение log3(3^x-6)=x-1 пожалуста!

[latex] log_3(3^x-6)=x-1 [/latex] ОДЗ: [latex]3^x-6\ \textgreater \ 0[/latex] [latex]3^x\ \textgreater \ 6[/latex] [latex]3^x\ \textgreater \ 3^{log_36[/latex] [latex]x\ \textgreater \ {log_36[/latex] [latex]log_3(3^x-6)=log_33^{ x-1 [/latex] [latex]3^x-6=3^{ x-1 [/latex] [latex]3^x-6-3^{ x-1} =0[/latex] [latex]3^x-3^{ x-1} =6[/latex] [latex]3^x(1-3^{-1}) =6[/latex] [latex]3^x* \frac{2}{3} =6[/latex] [latex]3^x* \frac{2}{3} =6[/latex] [latex]3^x =6* \frac{3}{2} [/latex] [latex]3^x =3^2[/latex] [latex]x=2[/latex] Ответ: 2