Solving two exponential equations

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Marsha Parmar
Marsha Parmar on 30 Jul 2023
Commented: Walter Roberson on 31 Jul 2023
I want to solve these two exponential equations with two unknowns.
5021747384670633/8796093022208 - (191*exp(-609699130650934272/(622444614725399*T)))/10 - (19*exx)/5
3227532116765295/4398046511104 - (159*exp(-3013775930722772480/(5602001532528591*T)))/10 - (27*exx)/5
Plaese help.

Answers (1)

Torsten
Torsten on 30 Jul 2023
Edited: Torsten on 30 Jul 2023
syms T
eqn = 5/19*(5021747384670633/8796093022208 - (191*exp(-609699130650934272/(622444614725399*T)))/10) ==...
5/27*(3227532116765295/4398046511104 - (159*exp(-3013775930722772480/(5602001532528591*T)))/10)
eqn = 
Tnum = vpasolve(eqn)
Tnum = 
exx1 = subs(lhs(eqn),T,Tnum)
exx1 = 
129.48326876014043959603358902269
exx2 = subs(rhs(eqn),T,Tnum)
exx2 = 
129.48326876014043959603358902269
  2 Comments
Walter Roberson
Walter Roberson on 31 Jul 2023
Are the two expressions intended to equal each other? Or is it a pair of simultaneous equations in which each has an implicit == 0 ?
syms T
eqn = str2sym('[5021747384670633/8796093022208 - (191*exp(-609699130650934272/(622444614725399*T)))/10 - (19*exx)/5, 3227532116765295/4398046511104 - (159*exp(-3013775930722772480/(5602001532528591*T)))/10 - (27*exx)/5]')
eqn = 
Tnum = vpasolve(eqn)
Tnum = struct with fields:
T: -690.72238711814271539481565981433 exx: 129.48326876014043959603358902269

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