Light values are linear, but our eye see logarithmically.  Get it?

The best explanation is that if you 8 lights of equal brightness, turn only 1 on, you will see a linear level of 1 light.  Turn 2 on, the linear value doubles, and appears to the eye about twice as bright.  But if you turn on 3 it will not seem 3 times as bright, that would require 4.  And to get 4 times as bright, to your eye, you would need all 8.  And so on.

Linear        Log (like our eyes or film stock reacts)

  1                1 

  2                2

  4                3

  8                4

16               5

So keeping all these 16 linear numbers becomes pointless if you only notice 5, your eyes can’t tell the difference.  What Log storage allows you do is keep better information that where you CAN tell the difference, a much smaller amount of data, but with nothing necessarily lost.  A simplified example to be sure.

This is destined to take over codecs because computers will handle the math.

Log Codecs

DPX - Arri Log C - Sony S Log

A video codec might use Log space to keep it’s information, as it has much more info, more latitude, which is great for color grading.  It must be converted to look natural on most monitors (which is a type of color grading).  This is going to be more and more popular as the information rivals Raw formats, but is much faster to work with.  A good compromise.  Some times Raw formats will convert to Log codecs for final coloring.