Question

log3 (2x-7) >= 2 log3(x+1) - log3(x-19)​

Answer 1

ОДЗ

2x-7>0; x>3.5

x+1>0;x>-1

x-19.0; x>19

общая ОДЗ x>19

log(3)(2x-7)-2log(3)(x+1)+log(3)(x-19)≥0

log(3)((2x-7)(x-19)/(x+1)^2))≥0

(2x-7)(x-19)/(x+1)^2≥1

(2x-7)(x-19)/(x+1)^2-1≥0

(2x^2-38x-7x+133-x^2-2x-1)/(x+1)^2≥0

(x^2-47x+132)/(x+1)^2≥0

(x-44)(x-3)/(x+1)^2≥0

----(-1)+++[3]----[44]+++

учитывая ОДЗ ответ x=[44;+∞)