document.write( "Question 1162782: 4.3093 = -(ln(ln T/(T-1)) solve for T? \n" ); document.write( "
Algebra.Com's Answer #786665 by Theo(13342)\"\" \"About 
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monster problem, but i think i have it.
\n" ); document.write( "the formula to solve is:
\n" ); document.write( "4.3093 = -ln(ln(T/(T-1))) which can be shown as 4.3093 = \"-ln%28ln%28T%2F%28T-1%29%29%29\".
\n" ); document.write( "to begin with, i let x = ln(T/(T-1))
\n" ); document.write( "the equation became:
\n" ); document.write( "4.3093 = -ln(x)
\n" ); document.write( "i solved for ln(x) to get ln(x) = -4.3093.
\n" ); document.write( "this is true if and only if e^(-4.3093) = x
\n" ); document.write( "this made x = .0134429564.
\n" ); document.write( "since x = that, and since x = ln(T/(T-1)), then i got:
\n" ); document.write( "ln(T/(T-1)) = .0134429564.
\n" ); document.write( "this is true if and only if T/(T-1) = e^.0134429564 = 1.013533719.
\n" ); document.write( "i multiplied both side of the equation by (T-1) to get:
\n" ); document.write( "T = 1.013533719 * (T - 1)
\n" ); document.write( "this was simplified to:
\n" ); document.write( "T = 1.013533719 * T - 1.013553719
\n" ); document.write( "i added 1.0135533719 to both side of the equation and i subtracted T from both side of the equation to get:
\n" ); document.write( "1.013553719 = 1.013533719 * T - T
\n" ); document.write( "i factored out T in the right side of the equation to get:
\n" ); document.write( "1.013553719 = T * (1.0135533719 - 1)
\n" ); document.write( "i simplified to get:
\n" ); document.write( "1.013553719 = T * .0135533719
\n" ); document.write( "i solved for T to get:
\n" ); document.write( "T = 1.013553719 / .0135533719 = 74.88951907\r
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\n" ); document.write( "\n" ); document.write( "if i did this correctly, this should be my answer.
\n" ); document.write( "to confirm, i replaced T in the original equation to see what the result would be.
\n" ); document.write( "the original equation was:
\n" ); document.write( "4.3093 = -ln(ln(T/(T-1)))
\n" ); document.write( "replacing T with 74.88951907, the equation becomes:
\n" ); document.write( "4.3093 = -ln(ln( 74.88951907/( 74.88951907-1)))
\n" ); document.write( "this becomes 4.3093 = 4.3093, confirming the value of T is correct.\r
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