Difference between revisions of "2006 AIME I Problems/Problem 9"
Ninja glace (talk | contribs) (→Solution) |
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<math>a^{12}r^{66}=8^{2006}</math> | <math>a^{12}r^{66}=8^{2006}</math> | ||
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+ | <math>a^{12}r^{66}=(2^3)^{2006}</math> | ||
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+ | <math>a^{12}r^{66}=2^{6018}</math> | ||
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+ | <math>a^{2}r^{11}=2^{1003}</math> | ||
== See also == | == See also == |
Revision as of 14:53, 3 August 2006
Problem
The sequence is geometric with
and common ratio
where
and
are positive integers. Given that
find the number of possible ordered pairs
Solution
We must now use the rules of logarithms: