Results 1 to 3 of 3

Math Help - anyone help???

  1. #1
    Junior Member
    Joined
    Jan 2007
    Posts
    36

    anyone help???

    i have

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

    and i need to find a value of t
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    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:

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

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

    EB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,184
    Thanks
    403
    Awards
    1
    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.)

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

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

    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.

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

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

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

    1.0013026573 (T - 1) = T

    1.0013026573T - 1.0013026573 = T

    0.0013026573T = 1.0013026573

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

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

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

    -Dan
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum