Question

log2(5x-9) меньше или равно log2(3x+1)
Помогите пожалуйста!

Answer 1

ОДЗ
$left { {{5x-9 textgreater 0} atop {3x+1 textgreater 0}} right. left { {{x textgreater 1.8} atop {x textgreater - frac{1}{3} }} right. \ \ x textgreater 1.8$

$log_2(5x-9) leq log_2(3x+1) \ \ 5x-9 leq 3x+1 \ \ 5x-3x leq 1+9 \ \2x leq 10 \ \ x leq 5$

x∈(1.8; 5]
Ответ: x∈(1.8; 5]