Question 29
For which natural numbers $n \gt 1$ does the expression
$$
\frac{\log_{10} 2 \cdot \log_{10} 3 \cdots \log_{10} n}{10^{n-1}}
$$
attain its smallest value? What is this value?
$$
\frac{\log_{10} 2 \cdot \log_{10} 3 \cdots \log_{10} n}{10^{n-1}}
$$
attain its smallest value? What is this value?