The system I'm considering is:

eqn2 = 
  {wB/(kB*T) + Log[(σB*AP)/(1 - σB*AP)] == 
   Log[(CP - (CB*σB*At + CH*σH*At))*vP] == 
   wH/(kB*T) + Log[(σH*AP)/(1 - σH*AP)]}

I want to find σB and σH as functions of everything else and then find CP when these densities have a threshold value of (P/L)*/al. Using Solve doesn't work, and I need my solution to scale up to handling a similar system with four equations and three unknown densities σB1, σB2 and σH. wB, wH, AP, At and vP are all known constants and CP, CB and CH are controlled variables. How would I proceed? Solve returns a blank list and I'm not sure how one would use FindRoot on this.


Your equation is a bit confusing. Can we rewrite it like this:

eqn1 = wB/(kB*T) + Log[(σB*AP)/(1 - σB*AP)];
eqn2 = Log[(CP - (CB*σB*At + CH*σH*At))*vP];
eqn3 = wH/(kB*T) + Log[(σH*AP)/(1 - σH*AP)];
Solve[{eqn1 == eqn2, eqn2 == eqn3}, {σH, σB}]

in which case it does solve for $\sigma$H and $\sigma$B, though the answer is ridiculously long.


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