Помогите решить логарифмическое неравенство срочно

$log_4log_{ \frac{1}{ \sqrt{2} } }(x+1) \ \textgreater \ 0,5 \\ \\ log_4log_{ \frac{1}{ \sqrt{2} } }(x+1) \ \textgreater \ log_4 4^\frac{1}{2} \\ \\ log_{ \frac{1}{ \sqrt{2} } }(x+1) \ \textgreater \ 2 \\ \\ log_{ \frac{1}{ \sqrt{2} } }(x+1) \ \textgreater \ log_{ \frac{1}{ \sqrt{2} } }( \frac{1}{ \sqrt{2} } )^2 \\ \\ x+1\ \textgreater \ \frac{1}{2} \\ \\ x\ \textgreater \ -0,5$

ОДЗ: 1) x + 1 > 0; x > -1
2)
$log_{ \frac{1}{ \sqrt{2} }} (x+1) \ \textgreater \ 0 \\ \\ x+1 \ \textless \ 1 \\ \\ x\ \textless \ 0$

Ответ: x∈(-1; -0,5)