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Complete Logarithmic forumlas

  1. Mar 9, 2009 #1
    1. The problem statement, all variables and given/known data
    I need to find as much as a complete logarithmic formulas worksheet or tutorials

    I have not been in school for atleast 2 semesters and the class im taking right now makes use of the basic logarithmic functions, not to complicated from what the teacher has told us. I do not remeber anything about logarithms tho so i need to refresh my memory. Im looking for the basic logarithmic formulas(properties) maybe from a website link, a worksheet or a tutorial site online? I appreciate the help.
     
  2. jcsd
  3. Mar 9, 2009 #2

    Tom Mattson

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    Here ya go...

    The most basic formula is the equivalence between exponental and logarithmic equations:

    [itex]y=a^x[/itex] if and only if [itex]log_a(y)=x[/itex]

    Next we have:

    [itex]\log_b(xy)=\log_b(x)+\log_b(y)[/itex]
    [itex]\log_b\left(\frac{x}{y}\right)=\log_b(x)-\log_b(y)[/itex]

    Verbally these say that the log of a product is equal to the sum of the logs of the factors, and that the log of a quotient equals the difference of the logs of the numerator and denominator.

    There is also:

    [itex]\log_b\left(a^x\right)=x\log_b(a)[/itex]

    This says that a power inside of a log can be brought out front as a coefficient. A special case of this is when [itex]a=b[/itex]:

    [itex]\log_b\left(b^x\right)=x\log_b(b)=x[/itex]

    The last step is justified because [itex]\log_b(b)=1[/itex].

    Finally we have the so-called "change of base" formula:

    [tex]\log_a(x)=\frac{\log_b(x)}{\log_b(a)}[/tex]
     
  4. Mar 9, 2009 #3
    Thanks for the post and for the explanation. :)
     
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