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August 31st, 2010, 09:49 AM  #1 
Newbie Joined: Aug 2010 Posts: 3 Thanks: 0  Logarithms and Reversing them
Not sure if this is the right area.... been out of math for awhile. Log10(P) =( A  (B / T)  (C * Log10(T)) + (D * T) + (( E * (F  T)) / F * T) * Log10(F  T)) Formula for r22 temperature to pressure conversion Where if T = 50 then P = 85 (rounded) Now I am trying to reverse it to Get T from P, according to Antoine Equation for pressure temperature relations T = (B / (A  Log10(P)))  C But I can't figure out the rest of the reverse equation to get the Temperature from the Pressure A = 29.35754453 B = 3845.1931152 C = 7.86103122 D = 0.002190939044 E = 305.8268131 F = 686.1 This are the Fixed Coefficients for the Whole Calculations if anyone needs them... Thanks, C.W. 
August 31st, 2010, 12:24 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Logarithms and Reversing them
There isn't going to be any nice inverse formula. I'm not even sure if you could solve it explicitly with Lambert's W. The best way would be with a numerical method like the secant method or Brent's method.

August 31st, 2010, 09:59 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,882 Thanks: 1835 
Problem already posted and replied to here: viewtopic.php?f=13&t=15557 so topic locked. 

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