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Thread: exp(log(3))=3 or e^ln(3)=3, why?

  1. #1
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    exp(log(3))=3 or e^ln(3)=3, why?

    exp(log(3))=3 or e^ln(3)=3, why?

    I am reading an explanation like this:
    "3 is the end result of growing instantly (using e) at a rate of ln(3). 3 = e^ln(3)"

    BUT I cannot understand it... actually I don't understand so well, e as well ln ... please try to explain me while keeping this things in the mind - THANKS
    Last edited by mr fantastic; Mar 26th 2011 at 03:20 PM. Reason: Copied title into main body of post.
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  2. #2
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    From the definition of a logarithm: $\displaystyle y = log_a b \implies b = a^y$

    When $\displaystyle a=b$ you get $\displaystyle y = log_a(a) \implies a = a^y \equiv a^1=a^y \equiv y=1$

    Hence $\displaystyle log_a a =1$ and since $\displaystyle \ln(x) = \log_e(x)$ then $\displaystyle e^{\log_e(x)} = x$


    ==========================

    Alternatively think of them as inverse operations which "cancel"
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