4. Solve the system of equations

$$
\left\{\begin{aligned}
\log _{x}(y+1) & =4 \log _{x+2} \sqrt{y-1} \\
\log _{y-1}(x+2) & =\log _{x}\left(\frac{x^{3}}{y+1}\right)
\end{aligned}\right.
$$
Answer: $\left(\frac{1+\sqrt{17}}{2}, \frac{7+\sqrt{17}}{2}\right),\left(\frac{5+\sqrt{17}}{2}, \frac{3+\sqrt{17}}{2}\right)$.