Решите неравенство

$Log_x( \sqrt{21-4x)}\ \textgreater \ 1$

ОДЗ:
$21-4x\ \textgreater \ 0$
$4x\ \textless \ 21$
$x\ \textless \ 5.25$

$x\ \textgreater \ 0; x \neq 1$

$ODZ (0;1) (1;5.25)$

1 случай

$0\ \textless \ x\ \textless \ 1$

$\sqrt{21-4x}\ \textless \ x^1$

$21-4x\ \textless \ x^2$

$x^2+4x-21\ \textgreater \ 0 D=16+84=100 x=-7; x=3$

Решений нет т.к. 0
2случай

1
$\sqrt{21-4x}\ \textgreater \ x^1$

$x^2+4x-21\ \textless \ 0$

1-7
Ответ (1;3)