log5(3x+1)>log5(x-2)

[tex]log_5(3x+1)\ \textgreater \ log_5(x-2)[/tex]

ОДЗ: [tex] \left \{ {{3x+1\ \textgreater \ 0} \atop {x-2\ \textgreater \ 0}} \right. =\ \textgreater \ \left \{ {{3x\ \textgreater \ -1} \atop {x\ \textgreater \ 2}} \right. =\ \textgreater \ \left \{ {{x\ \textgreater \ -\frac{1}{3}} \atop {x\ \textgreater \ 2}} \right. =\ \textgreater \ x\ \textgreater \ 2[/tex]

[tex]log_5(3x+1)\ \textgreater \ log_5(x-2)\\3x+1\ \textgreater \ x-2\\3x-x\ \textgreater \ -1-2\\2x\ \textgreater \ -3\\x\ \textgreater \ -\frac{3}2[/tex]

С учетом ОДЗ Ответ: [tex]x\ \textgreater \ 2[/tex]