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2014 AMC 12B Problems/Problem 20

Revision as of 17:48, 20 February 2014 by Kvnc1996 (talk | contribs)

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.

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