Question

log0.2(3x-5)>=log0.2(x+2)

Answer 1

$log_{0.2}(3x-5) geq log_{0.2}(x+2)$
ОДЗ:
$left { {3x-5 textgreater 0} atop {x+2 textgreater 0}} right.$
$left { {3x textgreater 5} atop {x textgreater -2}} right.$
$left { {x textgreater 1 frac{2}{3} } atop {x textgreater -2}} right.$
$x$ ∈ $(1 frac{2}{3} ;+$ ∞ $)$

$3x-5 leq x+2$
$3x-x leq 2+5$
$2x leq 7$
$x leq 3.5$

------------------------------[3.5]-------------------
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Ответ: $(1 frac{2}{3};3.5]$