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

2014 AMC 12B Problems/Problem 20

Revision as of 17:47, 20 February 2014 by Kvnc1996 (talk | contribs) (Created page with "The domain of the LHS implies that <cmath>40<x<60</cmath> Begin from the left hand side <cmath>log_{10}[(x-40)(60-x)]<2</cmath> <cmath>-x^2+100x-2500<0</cmath> <cmath>(x-50)^2>0<...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The domain of the LHS implies that \[40<x<60\] Begin from the left hand side \[log_{10}[(x-40)(60-x)]<2\] \[-x^2+100x-2500<0\] \[(x-50)^2>0\] \[x \not = 50\] Hence, we have integers from 41 to 49 and 51 to 59. There are 18 integers.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2014_AMC_12B_Problems/Problem_20&oldid=60095"