![image](https://tex.z-dn.net/?f=%5Clog_%7B0.2%7D%28-x%5E2%2B4x%2B5%29%3D%5Clog_%7B0.2%7D%28-x-31%29%5C%5C%0A%5Cbegin%7Bcases%7D-x%5E2%2B4x%2B5%3D-x-31%5C%5C%0A-x-31%3E0%5Cend%7Bcases%7D%5C%5C%0A%5Cbegin%7Bcases%7Dx%5E2-5x-36%3D0%5C%5Cx%3C-31%5Cend%7Bcases%7D%5C%5C%0A%5Cboxed%7Bx%5Cin%5Cvarnothing%7D)
0\end{cases}\\
\begin{cases}x^2-5x-36=0\\x<-31\end{cases}\\
\boxed{x\in\varnothing}" alt="\log_{0.2}(-x^2+4x+5)=\log_{0.2}(-x-31)\\
\begin{cases}-x^2+4x+5=-x-31\\
-x-31>0\end{cases}\\
\begin{cases}x^2-5x-36=0\\x<-31\end{cases}\\
\boxed{x\in\varnothing}" align="absmiddle" class="latex-formula">
Чтобы правая часть существовала, необходимо x < 7, а для левой - x > 7. Решений нет.