Question

log3(12-2x-x2)2
$log_3(12 - 2x - \times ^{2} ) > 2$

Answer 1

$log_3(12 - 2x - \times ^{2} ) \ \textgreater \ 2 \\ \\ ODZ:12-2x-x^2\ \textgreater \ 0 \\ x^2+2x-12\ \textless \ 0 \\ D=4+4*12=52 \\ x_{1} =(-2+ \sqrt{52} )/2;x_{2} =(-2- \sqrt{52} )/2; \\ \\ x\in((-2- \sqrt{52} )/2;(-2+ \sqrt{52} )/2) \\ \\ log_3(12 - 2x - \times ^{2} ) \ \textgreater \ log_39 \\ \\ 3\ \textgreater \ 1 \\ \\ 12-2x-x^2\ \textgreater \ 9 \\ \\ x^2+2x-3\ \textless \ 0 \\ \\ D=16; x_{1} =(-2-4)/2=-3;x_{2} =(-2+4)/2=1 \\ \\ +++(-3)---(1)+++ \\ \\OTVET: x\in(-3;1)$