# How to measure if data conforms to logarithmic curve

I am collecting data that should closely resembles a logarithmic curve. I have many datasets.

How can I measure how closely each dataset resembles a logarithmic curve and call out any outlying data points?

Here is an example of a curve that would represent my dataset:

There's an easy, non-statistical approach to the problem of measuring the speed of an object for which you have high-resolution position information like this. Say $x$ is a vector of (one-dimensional) positions and $t$ is a vector of times, such that after $t_i$ seconds have passed, the object is at $x_i$. You can estimate the object's speed at any time $t_i$ as $(x_{i+1} - x_i)/(t_{i+1} - t_i)$. The resemblance of this formula to the derivative of $x$ with respect to $t$ is not coincidental.