# How to use fzero to solve for a variable in an exponent?

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Danse Groom on 15 Feb 2020
Edited: Walter Roberson on 22 Feb 2020
I am trying to use fzero to find where two equations are equal to one another with respect to T, by setting them equal to one another and then subtraction one side from the other, f(t) - g(t) = 0. When I run the code posted below I dont get any error messages but nothing is printed out. Any Help would be greatly appreciated.
X1 = 0.5;
X2 = 0.5;
A12 = 1.6798;
A21 = 0.9227;
AW = 7.96681;
BW = 1668.21;
CW = 228.00;
AE = 8.04494;
BE = 1554.3;
CE = 222.65;
P = 763.712697;
gam1 = exp(A12*((A21*X2)/(A12*X1+A21*X2))^2);
gam2 = exp(A21*((A12*X1)/(A12*X1+A21*X2))^2);
function y = f(T)
y = gam1*X1*10^(AE - BE/(T+CE)) + (gam2*X2*10^(AW - BW/(T+CW))-P);
fun = @f; % function
T0 = 2; % initial point
z = fzero(fun,T0)
end

Star Strider on 15 Feb 2020
Take the fzero call out of the function it calls:
X1 = 0.5;
X2 = 0.5;
A12 = 1.6798;
A21 = 0.9227;
AW = 7.96681;
BW = 1668.21;
CW = 228.00;
AE = 8.04494;
BE = 1554.3;
CE = 222.65;
P = 763.712697;
gam1 = exp(A12*((A21*X2)/(A12*X1+A21*X2))^2);
gam2 = exp(A21*((A12*X1)/(A12*X1+A21*X2))^2);
function y = f(T)
y = gam1*X1*10.^(AE - BE./(T+CE)) + (gam2*X2*10.^(AW - BW./(T+CW))-P);
end
fun = @f; % function
T0 = 2; % initial point
z = fzero(fun,T0)
to get:
z =
80.0550
I also vectorised the ‘y’ assignment.

Danse Groom on 22 Feb 2020
Thank you!
Star Strider on 22 Feb 2020
My pleasure!