Неравенства 11 класс Срочно Сколько успеете

21.
ОДЗ: x-1>0 2x-4>0
x>1 2x>4
x>2
В итоге x∈(2; +∞)

log₂ (x-1)² - log₂ (2x-4) > log₂ 2
log₂ {(x-1)² / (2x-4)} > log₂ 2
$\frac{(x-1)^2}{2x-4} \ \textgreater \ 2 \\ \frac{(x-1)^2}{2x-4} -2\ \textgreater \ 0 \\ \frac{x^2-2x+1-2(2x-4)}{2x-4}\ \textgreater \ 0 \\ \frac{x^2-2x+1-4x+8}{2(x-2)}\ \textgreater \ 0 \\ \frac{x^2-6x+9}{2(x-2)}\ \textgreater \ 0 \\ \frac{(x-3)^2}{2(x-2)}\ \textgreater \ 0 \\ (x-3)(x-3)(x-2)\ \textgreater \ 0 \\ x=3 x=2$
- + +
---------- 2 --------- 3 -------------
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x=4 + + + | +
x=2.5 - - + | +
x= 0 - - - | -

x∈(2; 3)U(3; +∞)
Ответ: (2; 3)U(3; +∞)