Is there a way to find an arbitrary function that goes through two points x1,y1 and x2,y2?
Similar to the straight line:
(y1-y0) = m (x1-x0)
where m is the slope
Can we do this for any function?
For example y=ln(x)?
For a linear function, we have a system of 2 eq:

$<br /> y_1 = ax_1 + b <br />$

$<br /> y_2 = ax_2 + b <br />$


So we solve for a then for b, that's easy. Can we do the same for ln?
Where should a and b go? Like this?
$<br /> y_1 = a \cdot ln(bx_1)<br />$
$<br /> y_2 = a \cdot ln(bx_2) <br />$

I can solve this for a:
$$<br /> a = \frac{y_1 - y_2}{ln(\frac{x_1}{x_2})}<br />$$

but how do I solve for b???
Does this whole approach even make sense??