how to solve an exponential equation with one unknown in matlab

I have an equation that need to be solved for rs, and I could'nt get the answer in matlab I have values for the other parameters and I need to get rs. But when computing it on MATLAB I dont get a correct answer This is the equation

exp((-pi*ra)/rs)+exp((-pi*rb)/rs)=1

ra=90.82*10^6 rb=90.23*10^6 so only rs in unknown

[James Tursa]

Why didn't you continue with your other post?

https://www.mathworks.com/matlabcentral/answers/411188-how-to-solve-for-a-variable-in-an-exponential-equation

Answer 1

[Abraham Boayue]

Try the following code which uses Newton's method to find the root of the f(x) = 0.

close all;
clc;
N = 50;
ra = 90.82e6;
rb = 90.23e6;
a = pi*ra;
b = pi*rb;
tol = 1e-10;
x0 = 0;
x  = x0;
xn = x;
for k = 1:N
f  = exp(-a*x) + exp(-b*x)-1;
fd = -(a*exp(-a*x) + b*exp(-b*x));

      x = x-f/fd;
      err = abs(x-xn);
      xn = x ;
      if err<tol
          break;
      end

end
rs = 1/xn;
disp(rs)

Answer 2

[madhan ravi]

%Try this:

syms rs

ra=90.82*10.^6

rb=90.23*10.^6

rs=vpasolve(exp((-pi.*ra)./rs)+exp((-pi.*rb)./rs)-1,rs)