MathDB
\log_n 2 \cdot \log_n 4 \cdot \log_n 6 \ldots \log_n (2n - 2) \leq 1.

Source: Polish MO Recond Round 1982 p3

September 9, 2024
logarithmalgebrainequalities

Problem Statement

Prove that for every natural number n≥2 n \geq 2 the inequality holds log⁡n2⋅log⁡n4⋅log⁡n6…log⁡n(2n−2)≤1. \log_n 2 \cdot \log_n 4 \cdot \log_n 6 \ldots \log_n (2n - 2) \leq 1.
Back to ProblemsView on AoPS