Abdullah AL Shohag

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"An equation for me has no meaning, unless it expresses a thought of God" - S. Ramanujan

Defining negative value of logarithms

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If we consider  , then   but   will be negative only when   where   (for simplicity we will take  , so  )

 

      

  /*   */

 

 

if we put the value of   in the marked line,

 

 

so if we generalize it for any base, we get,

 , where