find unknown in equation using solve

I'm trying to find the value of Tb from the equation. but when i tried to run this code. I was not able to get the value

Bvals = [16.043;30.07;44.097;58.123;58.123;72.15;72.15;86.1754;100.2019;114.2285;128.2551;142.2817;156.3083;170.3348;184.3614;198.388;212.4146;226.4412;240.4677;254.4943;268.5209;612];
syms B Tb
sol = solve(B == (581.96*Tb^0.97476*(0.893^6.51274)*exp(((5.43076*10^-3)*Tb)-(9.53384*0.893)+((1.11056*10^-3)*Tb*0.893))),Tb);
vpa( subs(sol.', B, Bvals.') )

[Aditya Adhikary]

When I run the following code,

syms B Tb
Bvals = [16.043;30.07;44.097;58.123;58.123;72.15;72.15;86.1754;100.2019;114.2285;128.2551;142.2817;156.3083;170.3348;184.3614;198.388;212.4146;226.4412;240.4677;254.4943;268.5209;612];
eqn1 = B == (581.96*Tb^0.97476*(0.893^6.51274)*exp(((5.43076*10^-3)*Tb)-(9.53384*0.893)+((1.11056*10^-3)*Tb*0.893)))
sol = solve(eqn1,Tb,'IgnoreAnalyticConstraints', true);

it gives me an output

eqn1 =

B == (62709197696165713583*Tb^(24369/25000)*exp((370231346317807487*Tb)/57646075230342348800 - 4792797782046133/562949953421312))/22

suggesting that this equation is incredibly hard to solve, or unsolvable. In fact, it does not run to completion. Please check if the equation you want to solve is indeed solvable or not.

[Walter Roberson]

Tb = 7023886036441063489536*LambertW(1156972957243148396875*225179981368524800^(631/24369)*62709197696165713583^(23738/24369)*B^(25000/24369)*exp(14977493068894165625/1714815926865494016)*(1/3066550881896166502584528862089179446939425312))*(1/46278918289725935875)

[Eiko Raid]

why do we rearrange the equation?

[Walter Roberson]

You are trying to find the general solution in terms of B when you do the solve() . That general solution (if it exists) would be of the general form Tb = f(B) for some function f() . That involves re-arranging the equation.

Unfortunately, MATLAB is weak on solving equations in terms of LambertW so it is not able to find the solution. I posted the solution extracted by a different software package.

You would not need to re-arrange the equation if you were to loop over the Bvals finding a numeric solution each time.