Ta có : \(n^{200}=\left(n^2\right)^{100};5^{300}=\left(5^3\right)^{100}=125^{100}\)
Để: \(n^{200}< 5^{300}\Rightarrow\left(n^2\right)^{100}< 125^{100}\Leftrightarrow n^2< 125\)\(\Leftrightarrow n=11\)
\(n^{200}< 5^{300}\) => \(\left(n^2\right)^{100}< 125^{100}\) => \(n^2< 125\) <=> \(11^2< 125\) => \(n=11\)