2005 AMC 10A Problems/Problem 13
Contents
[hide]Problem
How many positive integers satisfy the following condition:
Solution
We're given , so
(because all terms are positive) and thus
Solving each part separately:
So .
Therefore the answer is the number of positive integers over the interval which is
Solution 2
We're given .
Alternatively to solution 1, first deal with the first half: . Because the exponents are equal, we can ignore them and solve for : , or .
The second half: , or , which means .
Therefore and which contains the same number of elements as which clearly contains values or choice .
~JH. L
See also
2005 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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