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Consider the set of triples $(g_1,g_2,g)\in(\Bbb R^+)^3$ such that $$\log g=(\log g_1)(\log g_2)$$

Is there any geometric or information theoretic meaning behind such triples?

We have $$2\log g=2 (\log g_1)(\log g_2)=(\log(g_1g_2))^2-(\log(g_1))^2-(\log(g_2))^2$$

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    $\begingroup$ Where does the last identity come from? Perhaps some text is missing? $\endgroup$
    – John B
    Dec 30, 2015 at 11:25
  • $\begingroup$ $(a+b)^2-a^2-b^2=2ab$ $\endgroup$
    – user76479
    Dec 30, 2015 at 11:28
  • $\begingroup$ Then please add parentheses somewhere so that it becomes clear that the powers are outside $\endgroup$
    – John B
    Dec 30, 2015 at 11:29
  • $\begingroup$ It's the saddle $z = xy$ viewed on an exponential scale? $\endgroup$
    – Nik Weaver
    Dec 30, 2015 at 13:06
  • $\begingroup$ @NikWeaver i am looking for geometry that comes from information theory like packing or something like that $\endgroup$
    – user76479
    Dec 30, 2015 at 20:54

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