Question

Lg(5x-7) меньше или равно 3lg2

Answer 1

lg(5x-7)≤3*lg2
lg(5x-7)≤lg2³
lg(5x-7)≤lg8
основание логарифма а=8, 8>1. знак неравенства не меняем:
$left { {{5x-7 textgreater 0} atop {5x-7 leq 8}} right. left { {{5x textgreater 7} atop {5x leq 15}} right. left { {{x textgreater 1,7} atop {x leq 3}} right.$

x∈(1,4; 3]