2010 AMC 8 Problems/Problem 24
Problem
What is the correct ordering of the three numbers, ,
, and
?
Solution 1
Use brute force.
,
, and
.
Therefore,
is the answer. (Not recommended for this contest)
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
10^8
2^{24}
(2^3)^8=8^8
5^{12}
(5^{\frac{3}{2}})^8=(\sqrt{125})^8)
{10, 8, \sqrt{125}}
8<10<\sqrt{125}
\textbf{(A)}\ 2^{24}<10^8<5^{12}
See Also
2010 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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