Question

log1/3(x-1)>2, 1/3 в основании

Answer 1

$log_{ \frac{1}{3} }(x-1)\ \textgreater \ 2$
ОДЗ: $x-1\ \textgreater \ 0$
$x\ \textgreater \ 1$
$log_{ \frac{1}{3} }(x-1)\ \textgreater \ log_{ \frac{1}{3} } \frac{1}{9}$
$(x-1)\ \textless \ \frac{1}{9}$
$x\ \textless \ 1\frac{1}{9}$
С учетом ОДЗ
Ответ:$(1; 1\frac{1}{9} )$