Function $f(x)=\log x$ is given by table.
Using the Newton interpolation polynomial, find $\log 1044$.
It is not specified what type (first or second) of polynomial we need to use. Could someone show the procedure for this problem?
EDIT:
I have the following approximation, that doesn't involve Newton interpolation polynomial: $$f(c)=\frac{c-a}{b-a}(f(b)-f(a))+f(a);a=1040,b=1050,c=1044$$
From here, it follows that $f(c)=f(1044)\approx 3.01886957$.
Question: How to approximate $f(c)$ by using Newton interpolation polynomial?