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  1. #1
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    anyone help???

    i have

    6.644 = -ln[ln(T/T-1)]

    and i need to find a value of t
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  2. #2
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    Quote Originally Posted by question View Post
    i have

    6.644 = -ln[ln(T/T-1)]

    and i need to find a value of t
    Hello,

    to get rid of ln us e^x:

    $\displaystyle e^{e^{-6.644}}=\frac{T}{T-1}$

    Solve for T. I've got T = 768.66...

    EB
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by question View Post
    i have

    6.644 = -ln[ln(T/T-1)]

    and i need to find a value of t
    You're looking for t or T? (This isn't really as stupid a question as it sounds. Technically they are different variables, though here the meaning is clear enough.)

    $\displaystyle 6.644 = -ln \left [ ln \left ( \frac{T}{T-1} \right ) \right ] $

    $\displaystyle -6.644 = ln \left [ ln \left ( \frac{T}{T-1} \right ) \right ] $

    $\displaystyle e^{-6.644} = ln \left ( \frac{T}{T-1} \right ) $

    Ordinarily I would leave the LHS alone, but as the exponent is in decimal form and we are going to have a complicated form in the end, it is just easier to get a decimal expression. Note: I am going to keep a ridiculous number of digits in the expression until the final answer to make rounding errors as small as reasonable.

    $\displaystyle 0.001301809877 = ln \left ( \frac{T}{T-1} \right ) $

    $\displaystyle e^{0.001301809877} = \frac{T}{T-1}$

    Again going to the decimal expression:
    $\displaystyle 1.0013026573 = \frac{T}{T-1}$

    $\displaystyle 1.0013026573 (T - 1) = T$

    $\displaystyle 1.0013026573T - 1.0013026573 = T$

    $\displaystyle 0.0013026573T = 1.0013026573$

    $\displaystyle T = \frac{1.0013026573}{0.0013026573} \approx 768.662$

    If you prefer the exact expression is got the same way and is:

    $\displaystyle t = \frac{e^{e^{-6.644}}}{e^{e^{-6.644}} - 1}$

    -Dan
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