Find value of large number

\begin{align*}

B_2 &= 0.18525 \\

z &= 2.8 \times 10^{10} \\

H &= 3000175332800 \\

R &= \frac{z^{3/5}}{(\log(z))^{1/5}} \\

\\

\text{Substitute } z \text{ with } 2.8 \times 10^{10} \\

\\

R &= \left. \frac{z^{3/5}}{(\log(z))^{1/5}} \right|_{z = 2.8 \times 10^{10}} \\

\\

b &= \cdot (\exp(z_{\text{value}} \cdot -0.5) - 1) \cdot z^{\frac{6D - 15}{5}} \cdot \exp\left( \frac{B_2 (8D - 5) R}{3} \right)

\end{align*}

Could you fix this code, or do you have any ideas before I try it in MATLAB?

% Define the constants
B_2 = 0.18525;
H = 3000175332800;
D = 0.9999932;
z = 2.8 * 10^10;

% Define the expression for R
R = (log(z))^(3/5) / (log(log(z)))^(1/5);

% Display R
disp('R:');
disp(R);
RR = double(R);
disp('RR:');
disp(RR);

% Define the expression for b
b = (log(H/(2*pi)))^2 * (exp(-0.5 * z) - 1) * z^((6 * D - 15) / 5) * exp(B_2 * (8 * D - 5) * R / 3);

% Evaluate b
bb = double(b);

% Display b
disp('b:');
disp(b);
disp('bb:');
disp(bb);

Answer 1

[Steven Lord]

Use Symbolic Math Toolbox. Define your constants symbolically.

% Define the constants
B_2 = sym(0.18525);
H = sym('3000175332800');
D = sym(0.9999932);
z = sym(2.8) * 10^10;

I made no modifications below this line besides removing the blank line at the end of the code block.

% Define the expression for R
R = (log(z))^(3/5) / (log(log(z)))^(1/5);

% Display R
disp('R:');

R:

disp(R);

RR = double(R);
disp('RR:');

RR:

disp(RR);

    5.3485

% Define the expression for b
b = (log(H/(2*pi)))^2 * (exp(-0.5 * z) - 1) * z^((6 * D - 15) / 5) * exp(B_2 * (8 * D - 5) * R / 3);

% Evaluate b
bb = double(b);

% Display b
disp('b:');

b:

disp(b);

disp('bb:');

bb:

disp(bb);

  -3.0519e-16