Like many things in physics and physiology, linear relationships can be obtained by taking the logarithms of various quantities and making some plots. The response of the eyeball, for example, is logarithmic.
Audio response is also logarithmic, which is why sound engineers work in decibels.
Contemplate the graph below, which is a graph of my best runs since I turned 40, graphed as the pace in minutes per mile vs. the logarithm of the distance in miles. It gives a rather straight line from a quarter mile to 1.5 miles, but then all of a sudden there is a change of slope. In a way I can run 2 miles to 10 km at a pace faster that I'd predict from the shorter runs. A very similar graph could be obtained for world records, plotting the pace in minutes per kilometer vs. the logarithm of the distance in kilometers. Here's how my ability to run one mile has changed over the years, starting at age 14.7.