Minimize Product of Logarithms Expression

1925SpecialistAlgebraSequences & SeriesLogarithmic Equations

52. matematično tekmovanje srednješolcev Slovenije

For which natural numbers $n > 1$ does the expression $$ \frac{\log_{10} 2 \cdot \log_{10} 3 \cdots \log_{10} n}{10^{n-1}} $$ attain its minimum value? What is this value?

0 students attempted0% solvedRating 1925

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Minimize Product of Logarithms Expression

1925SpecialistAlgebraSequences & SeriesLogarithmic Equations

52. matematično tekmovanje srednješolcev Slovenije

For which natural numbers $n > 1$ does the expression $$ \frac{\log_{10} 2 \cdot \log_{10} 3 \cdots \log_{10} n}{10^{n-1}} $$ attain its minimum value? What is this value?

0 students attempted0% solvedRating 1925