SOLUTION: 4.3093 = -(ln(ln T/(T-1)) solve for T?

Question 1162782: 4.3093 = -(ln(ln T/(T-1)) solve for T?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
monster problem, but i think i have it.
the formula to solve is:
4.3093 = -ln(ln(T/(T-1))) which can be shown as 4.3093 = .
to begin with, i let x = ln(T/(T-1))
the equation became:
4.3093 = -ln(x)
i solved for ln(x) to get ln(x) = -4.3093.
this is true if and only if e^(-4.3093) = x
this made x = .0134429564.
since x = that, and since x = ln(T/(T-1)), then i got:
ln(T/(T-1)) = .0134429564.
this is true if and only if T/(T-1) = e^.0134429564 = 1.013533719.
i multiplied both side of the equation by (T-1) to get:
T = 1.013533719 * (T - 1)
this was simplified to:
T = 1.013533719 * T - 1.013553719
i added 1.0135533719 to both side of the equation and i subtracted T from both side of the equation to get:
1.013553719 = 1.013533719 * T - T
i factored out T in the right side of the equation to get:
1.013553719 = T * (1.0135533719 - 1)
i simplified to get:
1.013553719 = T * .0135533719
i solved for T to get:
T = 1.013553719 / .0135533719 = 74.88951907

if i did this correctly, this should be my answer.
to confirm, i replaced T in the original equation to see what the result would be.
the original equation was:
4.3093 = -ln(ln(T/(T-1)))
replacing T with 74.88951907, the equation becomes:
4.3093 = -ln(ln( 74.88951907/( 74.88951907-1)))
this becomes 4.3093 = 4.3093, confirming the value of T is correct.

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