\(n^{^{ }150}< 5^{^{ }225}\)
\(\Rightarrow n^{^{ }150}=\left(n^{ }^2\right)^{75}\)
\(\Leftrightarrow\left(n^2\right)^{75}< \left(5^3\right)^{75}\)
\(\Rightarrow n^2< 125\)
\(\Rightarrow\)\(n< 12\)
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