Problem 23 · 2009 Math Kangaroo
Stretch
Number Theory
number-systems
If a = 2²⁵, b = 8⁸ and c = 3¹¹, then
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Answer: E — c < b < a
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Hint 1 of 2
Rewrite everything with the same base or compare sizes directly.
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Hint 2 of 2
8⁸ is a power of 2; compare it to 2²⁵, and estimate 3¹¹.
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Approach: convert to common bases and compare
- b = 8⁸ = 2²⁴ and a = 2²⁵, so a = 2·b, meaning b < a.
- c = 3¹¹ ≈ 177 000, far smaller than b = 2²⁴ ≈ 16.8 million.
- So c < b < a, which is option E.
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