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When Is This Logarithm Inequality True?

Algebra Level 1

True or False?

For all positive integers \(n \geq 2\),

\[ \log_{10} (n-1) + \log_{10} (n+1) < 2 \log_{10} n.\]

True only if \( n \leq 10 \) True only if \( n \leq 100 \) False always True always

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by Chung Kevin

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