Log5(3x+1)>log5(x-2)

[latex]log_5(3x+1) extgreater log_5(x-2)[/latex]ОДЗ: [latex] left { {{3x+1 extgreater 0} atop {x-2 extgreater 0}} ight. = extgreater left { {{3x extgreater -1} atop {x extgreater 2}} ight. = extgreater left { {{x extgreater -frac{1}{3}} atop {x extgreater 2}} ight. = extgreater x extgreater 2[/latex][latex]log_5(3x+1) extgreater log_5(x-2)\3x+1 extgreater x-2\3x-x extgreater -1-2\2x extgreater -3\x extgreater -frac{3}2[/latex]С учетом ОДЗ Ответ: [latex]x extgreater 2[/latex]