2 It is given that \(p = \mathrm { e } ^ { 280 }\) and \(q = \mathrm { e } ^ { 300 }\).
- Use logarithm properties to show that \(\ln \left( \frac { \mathrm { e } \mathrm { p } ^ { 2 } } { q } \right) = 261\).
- Find the smallest integer \(n\) which satisfies the inequality \(5 ^ { n } > p q\).