Question

Решить неравенства log2(x-1)< 1 (x-3)(x-1)> 0

Answer 1

$log_{2}(x-1)\ \textless \ 1$
$2\ \textgreater \ 1$
$x-1\ \textless \ 2^1$
$x-1\ \textless \ 2$
$x\ \textless \ 3$

$(x-3)(x-1)\ \textgreater \ 0$
$\left \{ {{x-3\ \textgreater \ 0} \atop {x-1\ \textgreater \ 0}} \right.$
$\left \{ {{x-3\ \textless \ 0} \atop {x-1\ \textless \ 0}} \right.$
$\left \{ {{x\ \textgreater \ 3} \atop {x\ \textgreater \ 1}} \right.$
$\left \{ {{x\ \textless \ 3} \atop {x\ \textless \ 1}} \right.$

x∈(-∞;1)∪(3;∞)
x<3

ответ: x ∈ (-∞;1)