How do I plot non linear equation in MATLAB?

Question

Equation:

0 = x*114 - x*log3(x) - 20.28*y 

I have Y = 10^3, 10^6, 10^9, 10^12, 10^15, ..... and above mentioned equation. How do I solve (ie getting values of x for different y) and plot this equation in MATLAB ?

Answer 1

Assuming that the solution is unique, one way to solve the equation is numerically:

y = 10.^(3:3:15);
opts = optimset( 'TolFun', 1e-9, 'TolX', 1e-9, 'MaxIter', 1e6, 'MaxFunEvals', 1e6 );
for ii = 1 : length(y);
  fcost = @(x)( x*114 - x*log10(x)/log10(3) - 20.28*y(ii) ).^2;
  xopt(ii) = fminsearch( fcost, y(ii), opts );
  fprintf( 1, 'y = %-5g : x = %-17.15g : f(xopt) = %-17.15g\n', ...
    y(ii), xopt(ii), fcost(xopt(ii)) );
end

% Plot the answers on a log-log scale.
loglog( xopt, y, 'k*' );

The above produces the following output, so we can see that the solutions are valid.

y = 1000  : x = 185.637624348601  : f(xopt) = 6.37079420013969e-17
y = 1e+06 : x = 197078.905034998  : f(xopt) = 8.88178419700125e-16
y = 1e+09 : x = 210030727.535742  : f(xopt) = 5.82076609134674e-11
y = 1e+12 : x = 224814576366.276  : f(xopt) = 1.52587890625e-05
y = 1e+15 : x = 241850436303022   : f(xopt) = 0                

There might be a better symbolic way to do it, but the above will work. I just guessed at the starting point for the search by setting it equal to y . If you need more accuracy in the solution, look at help optimset and help fminsearch . There are arguments that you can pass in that control the accuracy of the solution and when the search will terminate.