Question

Решите неравенство log5(3x+4)≤2

Answer 1

log₅(5x+4)≤2.   2=log₅5²=log₅25
 основание логарифма а=5, 5>1. знак неравенства не меняем
$left { {{3x+4 textgreater 0} atop {3x+4 leq 25}} right. , left { {{3x textgreater -4} atop {3x leq 21}} right. , left { {{x textgreater - frac{4}{3} } atop {x leq 7}} right.$

x∈(-4/3;7]