2005 AMC 12B Problems/Problem 17
Problem
How many distinct four-tuples of rational numbers are there with
Solution
Using the laws of logarithms, the given equation becomes
As must all be rational, and there are no powers of or in , . Then .
Only the four-tuple satisfies the equation, so the answer is .
See also
2005 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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All AMC 12 Problems and Solutions |
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