How to run Fsolve using vectors

Hi everyone. I am trying to run fsolve using vectors as inputs but it doesn't seem to work. My code is below. Do I have a syntax error?? I get x=[1 1 1 0.005348] as output. Seems that first 3 elements are just the same as initial condition. Any ideas?:

 a = [2 1 3 4];
 b = [-5 -10 -20 -30];
 for i = 1:length(a)

 F = @(x) ((log(x(i)^a(i)) - x(i)) - b(i));
 x0=[1 1 1 1];
 x = fsolve(F,x0,optimset('Display','none'));
 end

Answer 1

[Torsten]

a = [2 1 3 4];
b = [-5 -10 -20 -30];
F = @(x)log(x.^a)-x-b;
x0 = [1  1  1  1];
x = fsolve(F,x0,optimset('Display','none'));

Best wishes

Torsten.

[Fotis]

Thanks Torsten!

[BB]

Great script, helped me a lot!