Lg(x-1)<2 Log_2(2-x) <=3

$\displaystyle lg(x-1)\ \textless \ 2$

$ODZ (x-1)\ \textgreater \ 0; x\ \textgreater \ 1$

$\displaystyle lg(x-1)\ \textless \ 2$
$\displaystyle x-1\ \textless \ 10^2$
$\displaystyle x-1\ \textless \ 100$
$\displaystyle x\ \textless \ 101$
x∈ $(1;101)$

$\displaystyle log_2(2-x) \leq 3$

$ODZ 2-x\ \textgreater \ 0; x\ \textless \ 2$

$\displaystyle log_2(2-x) \leq 3 (2-x) \leq 2^3 (2-x) \leq 8 x \geq -6$

x∈ $[-6;2)$