Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2006 AIME I Problems/Problem 9"

(→‎Solution)
(→‎Solution)
Line 7: Line 7:
  
 
== Solution ==
 
== Solution ==
−
<math>\log(a1)+\log(a2)+\log(a3)+\cdots+\log(a12)=</math>
+
<math>\log(a1)+\log(a2)+\log(a3)+\ldots+\log(a12)=</math>
  
 
== See also ==
 
== See also ==

Revision as of 13:42, 3 August 2006

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2006_AIME_I_Problems/Problem_9&oldid=9154"