# anyone help???

• Jan 12th 2007, 11:38 AM
question
anyone help???
i have

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

and i need to find a value of t
• Jan 12th 2007, 11:58 AM
earboth
Quote:

Originally Posted by question
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
• Jan 12th 2007, 12:09 PM
topsquark
Quote:

Originally Posted by question
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