Question

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

Answer 1

$displaystyle lg(x-1) textless 2$

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

$displaystyle lg(x-1) textless 2$
$displaystyle x-1 textless 10^2$
$displaystyle x-1 textless 100$
$displaystyle x textless 101$
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∈ $[-6;2)$