Difference between revisions of "2010 AIME II Problems/Problem 5"
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== See also == | == See also == | ||
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Revision as of 23:37, 4 July 2013
Problem
Positive numbers ,
, and
satisfy
and
. Find
.
Solution
Using the properties of logarithms, by taking the log base 10 of both sides, and
by using the fact that
.
Through further simplification, we find that . It can be seen that there is enough information to use the formula
, as we have both
and
, and we want to find
.
After plugging in the values into the equation, we find that is equal to
.
However, we want to find , so we take the square root of
, or
.
See also
2010 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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