Question

Решить неравенство log 1/3 (2x+3)< log 1/3 ( х-1)

Answer 1

$log_{ \frac{1}{3} } (2x+3)\ \textless \ log_{ \frac{1}{3} } (x-1)$
ОДЗ:
$\left \{ {{2x+3\ \textgreater \ 0} \atop {x-1\ \textgreater \ 0}} \right. , \left \{ {{x\ \textgreater \ -1,5} \atop {x\ \textgreater \ 1}} \right.$
x∈(1;∞)
основание логарифма а=1/3, знак неравенства меняем:
2x+3>x-1, x>-4
$\left \{ {{x\ \textgreater \ 1} \atop {x\ \textgreater \ -4}} \right.$

x>1
x∈(1;∞)