![image](https://tex.z-dn.net/?f=%5Cdisplaystyle+16%5E%7Bx%2B1%7D%5C+%5Ctextgreater+%5C+4++%5C%5C+%284%5E%7B2%7D%29%5E%7Bx%2B1%7D%5C+%5Ctextgreater+%5C+4%5E%7B1%7D+%5C%5C+4%5E%7B2%28x%2B1%29%7D%5C+%5Ctextgreater+%5C+4%5E%7B1%7D+%5C%5C+4%3E1%3D%3E+2%28x%2B1%29%5C+%5Ctextgreater+%5C+1+%5C%5C+x%2B1%5C+%5Ctextgreater+%5C+0%2C5+%5C%5C+x%5C+%5Ctextgreater+%5C+-0%2C5+)
1=> 2(x+1)\ \textgreater \ 1 \\ x+1\ \textgreater \ 0,5 \\ x\ \textgreater \ -0,5 " alt="\displaystyle 16^{x+1}\ \textgreater \ 4 \\ (4^{2})^{x+1}\ \textgreater \ 4^{1} \\ 4^{2(x+1)}\ \textgreater \ 4^{1} \\ 4>1=> 2(x+1)\ \textgreater \ 1 \\ x+1\ \textgreater \ 0,5 \\ x\ \textgreater \ -0,5 " align="absmiddle" class="latex-formula">
x∈(-0,5; ∞)
Ответ: (-0,5; ∞)