Question

Помогите с математикой

Answer 1

Ответ:

$x\in (2.5;6.5]$

Пошаговое объяснение:

$log_{0.5}(2x-5)\geq -3 \\\\log_{0.5}(2x-5)\geq log_{0.5}0.5^{-3}=log_{0.5}\big(\frac{1}{2}\big)^{-3}=log_{0.5}8 \\\\log_{0.5}(2x-5)\geq log_{0.5}8 \\\\2x-5\leq 8\\\\2x\leq 13 \\\\x\leq 6.5$

ОДЗ:

$2x-5>0\\\\2x>5 \\\\x>2.5$

$Ansver: x\in (2.5;6.5]$