2006 AIME I Problems/Problem 9

Revision as of 14:42, 3 August 2006 by Ninja glace (talk | contribs) (Solution)

Problem

The sequence $a_1, a_2, \ldots$ is geometric with $a_1=a$ and common ratio $r,$ where $a$ and $r$ are positive integers. Given that $\log_8 a_1+\log_8 a_2+\cdots+\log_8 a_{12} = 2006,$ find the number of possible ordered pairs $(a,r).$



Solution

$\log(a1)+\log(a2)+\log(a3)+\ldots+\log(a12)=$

See also