## Problem of the Day #97: Logs and Products and Roots
*June 24, 2011*

*Posted by Albert in : potd , trackback*

There are $n$ numbers $a_i$ such that $a_i \in (1,\infty)$ for all $a_i$. Given:

$$\prod\limits_{i=1}^{n} \sqrt[n]{a_i^5} = 1000$$

Find the maximum possible value of:

$$25\sqrt[n]{\log_{10}(a_1) \times \log_{10}(a_2) \times \cdots \times \log_{10}(a_n)}$$

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