Question

Решите неравенство... lg^2 x-2lg x >3

Answer 1

$OD3:x\ \textgreater \ 0\\lg^2x-2lgx-3\ \textgreater \ 0\\lg^2x-2lgx-3=0\\\begin{cases}lgx_1+lgx_2=2\\lgx_1*lgx_2=-3\end{cases}\\lgx_1=-1\ \ \ \ \ \ ;lgx_2=3\\x_1=0,1\ \ \ \ \ \ \ \ \ x_2=1000\\///(+)///(0,1)...(-)...(1000)///(+)///\ \textgreater \ x\\(0)////////////////////////////////\ \textgreater \ x\\x\in(0;0,1)\cup(1000;+\infty)\\OTBET:0\ \textless \ x\ \textless \ 0,1;x\ \textgreater \ 1000$