Difference between revisions of "2006 AIME I Problems/Problem 9"
Ninja glace (talk | contribs) (→Solution) |
Ninja glace (talk | contribs) (→Solution) |
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<math>\log_8 a_1+\log_8 a_2+\ldots+\log_8 a_{12}= | <math>\log_8 a_1+\log_8 a_2+\ldots+\log_8 a_{12}= | ||
\log_8 a+log_8 (a*r)+\ldots+\log_8 (a*r^{11})</math> | \log_8 a+log_8 (a*r)+\ldots+\log_8 (a*r^{11})</math> | ||
| + | We must now use the rules of logarithms: | ||
| + | <math>\log_8 a_1+\log_8 a_2+\ldots+\log_8 a_{12}= | ||
| + | \log_8 (a*ar*ar^2*\cdots*ar^{11}*ar^{12}</math> | ||
== See also == | == See also == | ||
Revision as of 13:48, 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:
