'solve' not working as expected for Log Equations

Not sure why the first equation (f) cannot find a solution but the second (g) can? They are the same equation just in different forms.

Am I misunderstanding something about how the matlab solver works?

clc; clear
syms n k real
y=[.2;.6]; t=[280; 425];

f1= y(1)==1-exp(-k.*t(1).^n);
f2= y(2)==1-exp(-k.*t(2).^n);
Sol=solve(f1,f2)

g1= log(log(1/(1-y(1))))==n*log(t(1))+log(k);
g2= log(log(1/(1-y(2))))==n*log(t(2))+log(k);
Sol=solve(g1,g2)

Answer 1

[Walter Roberson]

if you vpasolve() and use a low enough start then it will find a solution

ss=vpasolve([f1,f2],[n,k], [.8999999040792;1])

The start point I show here is about the upper limit; for example .8999999040793 will not work.

[Jaquen Allen]

So the only way to solve in that form is to have an approx estimate of the values you're looking for? Appreciate the help!

[Walter Roberson]

.89 is pretty far from the actual value, on a relative scale.

clc; clear
syms n k real
y=[.2;.6]; t=[280; 425];

f1= y(1)==1-exp(-k.*t(1).^n);
f2= y(2)==1-exp(-k.*t(2).^n);
eqn = [f1,f2];
Sol = vpasolve(eqn, [n, k], [50;0]);
[Sol.n, Sol.k], subs(eqn, Sol)

ans = 

ans = 

Sol.n

ans = 

50.0

Sol = vpasolve(eqn, [n, k], [0;0]);
[Sol.n, Sol.k], subs(eqn, Sol)

ans = 

ans = 

It looks like too large of an initial guess leads to false solutions if it gives a solution at all.