How to findout this equations value

R*e^15b=35.75

R*e^25b=29.125

R*e^35b=22.875

I need to find out the value of R and b from above equaations. Is there any command in matlab to findout this calculation?

Answer 1

[John D'Errico]

That is impossible, since your equations are not written in unambiguous mathematics.

Is e^15b intended to mean exp(15*b)?

Is e^15b intended to mean exp(15)*b?

Is e the base of the natural logarithem? Thus

format long
exp(1)

ans = 
   2.718281828459045

Even if as I suspect, you actually have these equations:

syms R b
E1 = R*exp(15*b) == 35.75;
E2 = R*exp(25*b) == 29.125;
E3 = R*exp(35*b) == 22.875;

then no unique solution can possibly exist. That is, divide equation 2 by equation 1. That leaves us with

E2/E1

ans = 

As you can see, R goes away, and we could compute b from that relation.

vpa(solve(E2/E1))

ans = 

However, suppose we chose to do this instead?

E3/E1

ans = 

vpa(solve(E3/E1))

ans = 

And finally, we could do this:

vpa(solve(E3/E2))

ans = 

Which as you see, returns a completely different result for b. And when we do so, depending on the value of b we chose from how we might derive it, then R is also completely different.

Answer 2

[Saksham Gupta]

As per my understanding, you wish to solve the given equations

You may use the following code to solve them:

syms R b
eqns = [ R*exp(15*b) == 35.75 , R*exp(25*b) == 29.125 ];
a = solve( eqns , [ R ,b ] );
disp(a.R);
disp(a.b);

I am using 2 equations only as I am able to identify only 2 variables : 'R' and 'b'.

My output is:

You may refer to documentation of solve to learn more about it.

Answer 3

[Sam Chak]

Hi @Sourasis Chattopadhyay

You can try using the solve() command.

R12 = 48.6173;  % solving Eqn 1 and Eqn 2 simultaneously
R23 = 53.2756;  % solving Eqn 2 and Eqn 3 simultaneously
R31 = 49.9703;  % solving Eqn 3 and Eqn 1 simultaneously
b12 = -0.020495335725415202423043826631973699411349908259696363801512111;
b23 = -0.024155230072427962515559053432074702762580354955690539307109413;
b31 = -0.022325282898921582469301440032024201086965131607693451554310762;
x   = linspace(10, 40, 3001);
y1  = R12*exp(b12*x);
y2  = R23*exp(b23*x);
y3  = R31*exp(b31*x);
plot(x', [y1' y2' y3'], 'LineWidth', 1.5), grid on, hold on,
plot([15 25 35], [35.75 29.125 22.875], 'mo', 'MarkerSize', 12, 'LineWidth', 2), hold off
xlabel('x'), ylabel('y'), 
legend('y1', 'y2', 'y3')