finding a solver in matlab to solve an equation

I have an equation which is shown below:

2^((2*10^6)/x)-((1.5536*10^(-51)*x)/(2.6243*10^(-15)+((3.9810*10^(-21))*x)))=0

I could solve it with fzero with different numbers. But now when I run it with any types of numbers as a starting value for fzero solver it aborts search because faces with NaN.

Any one can help me to find a starting value to solve it with fzero or suggest me another solver to solve it.

thanks any one

Answer 1

[Star Strider]

I am not surprised that the numerical solvers are having problems with it!

syms x 
Eqn = 2^((2*10^6)/x)-((1.5536*10^(-51)*x)/(2.6243*10^(-15)+((3.9810*10^(-21))*x)));
Eqn = simplify(Eqn, 500)

Eqn = 

Sx = solve(Eqn)

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

Sx = 

Sxn = double(Sx)

Sxn = -2.5669e-50

.

Answer 2

[Matt J]

Well, you could plot the function to get an idea where to make your initial guess. To me, though, it doesn't look like it has any roots. It looks like it just decays asymptotically to 1:

 f=@(x)2.^((2*10^6)./x)-((1.5536*10^(-51)*x)./(2.6243*10^(-15)+((3.9810*10^(-21))*x)));
 x=logspace(10,16); semilogx(x,f(x));

[Walter Roberson]

syms x
Q = @(v) sym(v)

Q = function_handle with value:
    @(v)sym(v)

f = 2.^((Q(2)*10^6)./x)-((Q(1.5536)*10^(-51)*x)./(Q(2.6243)*10^(-15)+((Q(3.9810)*10^(-21))*x)))

f = 

 fplot(f, [-659210,-659200])

Answer 3

[Walter Roberson]

syms A B C x
Eqn = 2^(2*10^6/x) - A*10^(-51)*x/(B*10^(-15) + C*10^(-21)*x)

Eqn = 

sol = solve(Eqn,x)

Warning: Unable to find explicit solution. For options, see help.

 
sol =
 
Empty sym: 0-by-1
 

However, Maple says that it does have a solution, namely

sol_maple = 2000000*log(2)*B/(B*lambertw(1/500000000000000000000000000000*A*log(2)/B*4^(C/B)) - 2*C*log(2))

sol_maple = 

soln = subs(sol_maple, [A,B,C], [1.5536, 2.6243, 3.9810])

soln = 

solv = vpa(soln)

solv = 

simplify(subs(Eqn, [A,B,C,x], [1.5536, 2.6243, 3.9810, soln]))

ans = 

double(ans)

ans = 0.1221

I do not know why it does not cross-check... it cross-checks in Maple.