2005 AMC 12B Problems/Problem 17
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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 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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