Question

С11кл. решите неравенства 1) ln(6x-12)< 0 2) ln^2x - 2lnx - 3< 0

Answer 1

$1)ln(6x-12)\ \textless \ 0\\ ODZ:\\ x\ \textgreater \ 2\\ .............\\ 6x-12\ \textless \ e^0\\ 6x\ \textless \ 13\\x\ \textless \ \frac{13}{6} \\2\ \textless \ x\ \textless \ \frac{13}{6} 2)ln^2(x)-2ln(x)-3\ \textless \ 0\\x\ \textgreater \ 0\\............................\\ln(x)=t\\t^2-2t-3\ \textless \ 0\\t^2-2t-3=0\\t_1=-1\\t_2=3\\-1\ \textless \ t\ \textless \ 3\\-1\ \textless \ ln(x)\ \textless \ 3\\ \frac{1}{e}\ \textless \ x\ \textless \ e^3$