Mathematics

  ; Always remember for base, ,   (base cant be zero or negative or 1, it can be less than 1 . e.g. 3/2, 1/2) And for negative value log doesn't exist  (why??) Reason is simple we cant get any negative number even not get zero whatever be the power of a positive number. e.g.   ,  positive or negative what do you think ??? clearly positive. multiplying 1/2 , 55 times and get positive values. therefore,  so, whenever you see a logarithmic expression ,  ;  ,   and  Properties: 1.   ;  clearly, whatever be the value of "a",  2.  ;    , 3.   and  ;   4. Base changing formula:-  ( in second term you can take any base) Proof:  consider,   ;     ....................... (i)  (by definition) consider,    ;   let   and   ...................... (ii) ...