MathDB
Log Sum

Source: AIME 2010I Problem 14

March 17, 2010
floor functionlogarithmssearchinequalitiesfunctionalgebraAMC

Problem Statement

For each positive integer n, let f(n) \equal{} \sum_{k \equal{} 1}^{100} \lfloor \log_{10} (kn) \rfloor. Find the largest value of n for which f(n)≤300 f(n) \le 300. Note: ⌊x⌋ \lfloor x \rfloor is the greatest integer less than or equal to x x.
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