Problem
What is the correct ordering of the three numbers, , , and ?
문제 )
10^8 , 5^12 , 2^24 세수의 올바른 순서는 다음의 어느것 인가?
Solution 1
Use brute force. ,
,
and . Therefore,
is the answer.
Solution 2
Since all of the exponents are multiples of four, we can simplify the problem by taking the fourth root of each number. Evaluating we get , , and . Since
it follows that
is the correct answer.
Solution 3
First, let us make all exponents equal to 8. Then, it will be easy to order the numbers without doing any computations. is fine as is. We can rewrite as . We can rewrite as . We take the eighth root of all of these to get . Obviously,
so the answer is
풀이 1)
무작정 계산하기
10^8 은 100000000
5^12 는 244140625
2^24 는 16777216
2^24 < 10^8 < 5^12
답은 A
풀이 2)
지수 8, 12 ,24 의 최대공약수가 4 니까
10^8 = ( 10^2)^4 = 100^4
5^12 = ( 5^3 )^4 = 125^4
2^24 = ( 2^6)^4 = 64^4
64 < 100 < 125
니까
2^24 < 10^8 < 5^12
답은 A
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