\[\begin{array}{l}
\log _{25}^2\left( {x + 2} \right) - {\log _{\frac{1}{5}}}{\left( {x + 2} \right)^3} - 8 = 0\left( {DK:x > - 2} \right)\\
\Leftrightarrow \frac{1}{4}\log _5^2\left( {x + 2} \right) + 3{\log _5}\left( {x + 2} \right) - 8 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{\log _5}\left( {x + 2} \right) = - 6 + 2\sqrt {17} \\
{\log _5}\left( {x + 2} \right) = - 6 - 2\sqrt {17}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x + 2 = {5^{ - 6 + 2\sqrt {17} }}\\
x + 2 = {5^{ - 6 - 2\sqrt {17} }}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = {5^{ - 6 + 2\sqrt {17} }} - 2\\
x = {5^{ - 6 - 2\sqrt {17} }} - 2
\end{array} \right.
\end{array}\]
