Решите неравенство пожалуйста

$log_{2}^2(\sqrt{x+2}+1) + 2 \ \textgreater \ log_{2}(x\sqrt{x+2}+3x+5\sqrt{x+2}+7) \\ \sqrt{x+2}=t \ \textgreater \ 0\\ x=t^2-2 \\ log_{2}^2(t+1) + 2 \ \textgreater \ log_{2}((t^2-2)t+3(t^2-2)+5t+7) \\ log_{2}^2(t+1)+2 \ \textgreater \ log_{2}(t+1)^3 \\ log_{2}^2(t+1)+2\ \textgreater \ 3*log_{2}(t+1)\\ t\ \textgreater \ 0 \\ log_{2}(t+1)=y\\ y^2+2\ \textgreater \ 3y\\ y^2-3y+2\ \textgreater \ 0 \\ (y-1)(y-2) \ \textgreater \ 0 \\ y \in (-\infty ; 1 ) \ \cup \ (2; \infty) \\ x \in [-2;1) \ \ \cup \ \ (7;\infty)$