Логарифмическое неравенство, номер 2!

[latex]log_3(2-3^x)\ \textless \ x+1-log_34 \\ \\ log_3(2-3^x)+log_34\ \textless \ (x+1)\cdot log_33 \\ \\ log_3(2-3^x)\cdot 4\ \textless \ log_33^{x+1} \\ \\ \left \{ {{2-3^x\ \textgreater \ 0} \atop {(2-3^x)\cdot 4 \ \textless \ 3^{x+1} }} \right. [/latex] [latex] \left \{ {{2-3^x\ \textgreater \ 0} \atop {8-4\cdot 3^x \ \textless \ 3\cdot3^{x} }} \right. \\ \\ \left \{ {{3^x\ \textless \ 2} \atop {8\ \textless \ 7\cdot3^{x} }} \right. \\ \\ \frac{8}{7}\ \textless \ 3^x\ \textless \ 2 \\ \\ log_3{ \frac{8}{7}}\ \textless \ x\ \textless \ log_32 [/latex]