2020 · Q7
Which one of the following is the largest number among 2222², 222^22, 22^222, 2^2222?
Elementary MathematicsNumber System
- A2^2222
- B22^222
- C222^22
- D2222²
Explanation
Compare the logarithms: log₁₀(2222²) ≈ 6.7, log₁₀(222²²) ≈ 51.6, log₁₀(22²²²) ≈ 298, log₁₀(2²²²²) ≈ 668.8. The last is by far the largest, so 2²²²² is the largest of the four numbers. The enormous exponent 2222 outweighs the larger bases, since 2222·log₁₀ 2 ≈ 669 dwarfs the other logarithms.