Plot implicit function with log scale

Hello, I want to plot implicit function (33.9*k*M*x*y)/(k*M*sqrt(67.8*y)+33.9)-1.715369 = 0 with this constants.

N=1.715369;

M=4444.444444;

k=10^4;

I want to plot this implicit function at (x= 10^-15~10^-9) with log scale (both x and y)

Any help would be appreciated! Thanks.

[Bjorn Gustavsson]

Why can't you use fimplicit and then change to log-scale afterwards:

set(gca,'XScale','log','YScale','log')

HTH

Answer 1

[Walter Roberson]

In order to fimplicit this, you need to have an idea of what the y range is. It turns out that there are two solutions for each x, and they vary by roughly 10^40, making it difficult to plot unless you already have an idea of what you are looking for.

The solution with a smaller range is effectively constant over that range of x values.

syms k M x y
eqn = (33.9*k*M*x*y)./(k*M*sqrt(67.8*y)+33.9)-1.715369

eqn = 

N_val = sym(1.715369);
M_val = sym(4444.444444);
k_val = sym(10^4);

eqnn = subs(eqn, {M, k}, {M_val, k_val})

eqnn = 

ysol = solve(eqnn, y)

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

ysol = 

vpa(expand(ysol), 10)

ans = 

x_vec = logspace(-15, -9, 200);

y = double(subs(ysol, x, x_vec)).';

loglog(x_vec, y, '-b');

[Bjorn Gustavsson]

Since the OP gave us values for both M and N, one of the M's in the equation might be a typo.

[Bo Hoon Han]

I'm really thankful for your kind answer.