Question

решите неравенство
log3(x-1)<2

Answer 1

$log_3(x-1)\ \textless \ 2\; ,\; \; ODZ;\; \; x-1\ \textgreater \ 0\; ,\; \; x\ \textgreater \ 1\\\\log_3(x-1)\ \textless \ log_33^2\\\\x-1\ \textless \ 9\\\\x\ \textless \ 10\\\\ \left \{ {{x\ \textgreater \ 1} \atop {x\ \textless \ 10}} \right. \; \Rightarrow \; \; x\in (1,10)$