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For which positive integers n does the inequality 3ⁿ exceed n³?

1. n ≥ 2
2. n ≥ 3
3. n ≥ 4
4. n < 4

Correct answer: n ≥ 4

Solution

Check: n=1 (3>1) and n=2 (9>8) hold, n=3 gives 27=27 (not strictly greater) so it fails, and for n>=4 (81>64, ...) it always holds. The condition guaranteeing 3^n>n^3 for all such n is n>=4; 'n<4' is false since n=3 fails.

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