\(\begin{array}{l}
{\log _3}\left( {x + 2} \right) \ge 1 \Leftrightarrow \left\{ \begin{array}{l}
x + 2 > 0\\
x + 2 \ge 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x > - 2\\
x \ge 1
\end{array} \right. \Leftrightarrow x \ge 1
\end{array}\)