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Thread: logarithm help

  1. #1
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    logarithm help

    i have this equation

    $\displaystyle f = \frac{1-exp(-2s(1-x)}{1-exp(-2s)}*\frac{1}{x(1-x)}$

    when computing high values of $\displaystyle s$ i have problems as the exponential tends to very small numbers. Instead i want to take natural logs of this equation so i can avoid computing the exponentials

    how do i take logs such that the exponentials disappear
    Last edited by chogo; Aug 12th 2009 at 08:17 AM.
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  2. #2
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    Quote Originally Posted by chogo View Post
    $\displaystyle f = \frac{1-exp(-2s(1-x)}{1-exp(-2s)}*\frac{1}{x(1-x)}$
    Your stuff is hard to follow; you're missing a bracket; top line:
    1 - [-2s(1 - x)]^k (k = exponent)
    Is that what you mean?
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  3. #3
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    Quote Originally Posted by chogo View Post
    i have this equation

    $\displaystyle f = \frac{1-exp(-2s(1-x)}{1-exp(-2s)}*\frac{1}{x(1-x)}$

    when computing high values of $\displaystyle s$ i have problems as the exponential tends to very small numbers. Instead i want to take natural logs of this equation so i can avoid computing the exponentials

    how do i take logs such that the exponentials disappear
    Take it one step at a time and recall the following laws:

    $\displaystyle log(ab) = log(a) + log(b)$

    $\displaystyle log(a/b) = log(a) - log(b)$

    $\displaystyle log(a^k) = k \, log(a)$

    To start

    $\displaystyle ln(f) = ln(\frac{1-exp(-2s(1-x))}{1-exp(-2s)}) + ln(\frac{1}{x(1-x)})$

    $\displaystyle = ln(1-e^{-2s(1-x)}) - ln(1-e^{-2s}) - ln(x) - ln(1-x)$

    Note you can't simplify $\displaystyle ln(1-x)$ because $\displaystyle ln(a-b) \neq ln(a) - ln(b)$
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  4. #4
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    $\displaystyle f = \frac{1-e^{(-2s(1-x))}}{1-e^{(-2s)}}*\frac{1}{x(1-x)}$

    apologies wilmer this is the equation with brackets right

    thank you for taking the time to reply

    e^(i*pi) i understand the laws and how to expand such equations, my problem is that i need to rearrange the equations such that i do not end up with $\displaystyle ln(1-e^{(x)})$

    i am not sure if you understand what i mean. for very large values of $\displaystyle s$ when i compute the above formula i end up with numerical overflow problems. That is why i need to remove the exponentials. But i cant see a way of rearranging this formula so as to remove the exponentials.

    can it be done? any substitutions you think i should try

    thank you for your help
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