estimate the parameters of an equation

Hi there,

I have a question:

I have an equation like this: 45=a*5^b;

is there any way to estimate a and b only from this equation?

thanks

[Adam]

At a glance, without putting much thought into it I'd imagine there are an infinite number of solutions unless you are restricting yourself to integers only.

Answer 1

[Star Strider]

No.

You are estimating 2 parameters with 1 (x,y) data pair. There is no unique solution.

Answer 2

[Steven Lord]

Borrowing a problem from Cleve: "I'm thinking of two numbers. Their average is 3. What are the numbers?" I just wrote down my answer; I would be very surprised if you gave the same answer I wrote down.

Like Cleve's question, your question has infinitely many solutions. But if you want the solution for a in terms of b:

syms a b
f = 45 == a*5^b;
asol = solve(f, a)
check = isAlways(subs(f, a, asol))