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Find the Sum of All Solutions to 

 

\(\begin{align*} (\log_2 x)(\log_3 x)(\log_4 x)(\log_5 x) &= (\log_2 x)(\log_3 x)(\log_4 x) + (\log_2 x)(\log_3 x)(\log_5 x) \\ &\quad + (\log_2 x)(\log_4 x)(\log_5 x) + (\log_3 x)(\log_4 x)(\log_5 x). \end{align*}\)

 Mar 30, 2019
 #1
avatar+30629 
+3

Here's one solution:

 

 

(Of course, you don't have to use base 60; any base would do - but I only thought of this after doing the above!). 

.

 Mar 31, 2019
edited by Alan  Mar 31, 2019
edited by Alan  Mar 31, 2019
edited by Alan  Mar 31, 2019

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