Trying to solve a log equation with one variable help! ERROR: 1 equations in 2 variables. New variables might be introduced.

Hey, I'm trying to solve for one variable, T in two log functions.

syms T
pstarS=10^(7.06623-(1507.434/(T+214.979)))
pstarT=10^(6.95185-(1346.773/(T+219.693)))
total=pstarS+pstarT
eqn1=total==1
eval(solve(eqn1,T,65))

I'm really new to matlab, and this is the general form my prof used to solve example equations. I'm trying to solve for T, and matlab also warns me that 'an explicit solution could not be found'. I'm lost trying to troubleshoot this, any help would be great, thanks!

Answer 1

[Star Strider]

The correct syntax is:

syms T
pstarS=10^(7.06623-(1507.434/(T+214.979)));
pstarT=10^(6.95185-(1346.773/(T+219.693)));
total=pstarS+pstarT;
eqn1=total==1
T = solve(eqn1, T)

(the eval call not being necessary) but that's still taking the long way round.

A more direct implementation would use anonymous functions for pstarS, pstarT and total, and the fzero function for the solution:

pstarS = @(T) 10^(7.06623-(1507.434/(T+214.979)));
pstarT = @(T)10^(6.95185-(1346.773/(T+219.693)));
total = @(T) pstarS(T)+pstarT(T) - 1;

T = fzero(total, 1)

both producing:

T =

     -27.3354

EDIT — What your professor wants will not make it so, at least with those equations.

The plots:

pstarS = @(T) 10.^(7.06623-(1507.434./(T+214.979)));
pstarT = @(T)10.^(6.95185-(1346.773./(T+219.693)));
total = @(T) pstarS(T) + pstarT(T) - 1;

T = linspace(0,100,250);
figure(1)
plot(T, total(T),  T, pstarS(T),  T, pstarT(T))
grid
legend('total', 'pstarS', 'pstarT', 'Location','NW')

[Emily Petillo]

Ok, I understand what that function's doing now. Thanks!

[Star Strider]

My pleasure!