Difference between revisions of "2009 AIME II Problems/Problem 2"
(New page: == Problem == Suppose that <math>a</math>, <math>b</math>, and <math>c</math> are positive real numbers such that <math>a^{\log_3 7} = 27</math>, <math>b^{\log_7 11} = 49</math>, and <math...) |
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Revision as of 07:40, 7 April 2009
Problem
Suppose that ,
, and
are positive real numbers such that
,
, and
. Find
Solution
First, we have:
Now, let , then we have:
This is all we need to evaluate the given formula. Note that in our case we have ,
, and
. We can now compute:
Similarly, we get
and
and therefore the answer is .
See Also
2009 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |