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Logarithmic function as an integral

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data
    I'm attempting to prove the rules for the logarithmic function using the Integral definition: Log(x)=[1,x]∫1/t dt. I think im alright with the product rule but I'm struggling with the quotient rule: i.e. Log(a/b)=Log(a)-Log(b). I believe that I'm having trouble breaking up the Integral correctly. Any help would be appreciated!

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 18, 2011 #2


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    If you can show the product rule, then the quotient rule will follow the same logic, with an appropriate assumption about which of a or a/b is larger. Alternatively, use substitution to show that [itex]\log(1/b) = - \log b[/itex] so that you can combine this with the product rule.
  4. Nov 18, 2011 #3


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