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Find the sum of all solutions to \(\begin{align*} (\log_2 x)(\log_3 x)(\log_4 x)(\log_5 x) &= (\log_2 x)(\log_3 x)(\log_4 x) + (\log_2 x)(\log_3 x)(\log_5 x) \\ &\quad + (\log_2 x)(\log_4 x)(\log_5 x) + (\log_3 x)(\log_4 x)(\log_5 x). \end{align*}\)

 Apr 10, 2019
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The sum of the solutions is 37.

 Nov 30, 2019

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