Question

ПОМОГИТЕ решить неравенство, пожалуйста
Log x (1-2x)<1

Answer 1

$log_x(1-2x)\ \textless \ 1\\ D(y): \ x\ \textgreater \ 0, x \neq 1, 1-2x\ \textgreater \ 0\\ x\ \textgreater \ 0,x \neq 1, x\ \textless \ 0,5\\ x\in(0;0,5)\\ log_x(1-2x)\ \textless \ log_xx\\ 1-2x\ \textgreater \ x\\ -2x-x\ \textgreater \ -1\\ -3x\ \textgreater \ -1\\ \left \{ {{x\ \textless \ \frac{1}{3} } \atop {x\in(0;0,5)}} \right. \\ x\in(0; \frac{1}{3} )$