John, Paul and George received three boxes with apples and were ordered to get apples out of boxes and put them on the table. So they opened their boxes - each one opened one box - and started taking out the apples and putting them on the table.
While they were doing it, each one of them got a nice tune in his mind and went to write a song instead, thus, leaving his task unfinished. The original number of apples in each box was different. There were only 2 apples in Paul's box, 12 in John's box, and 22 in George's box. When all of them left their boxes, it turned out that there was only one apple left in each box.
If we use O to denote the original number of apples in a box, T to denote the number of apples taken out and L to denote the number of apples left, we will get this:
As we can see, the L is the same for each person, however, it does not at all mean that they were equally determined to finish their task. In fact, George was the most faithful one - he almost finished his job, while Paul stopped only half way through. In order to see each person's faithfulness toward completing his task (let's denote it by F) we might need to divide T by O. This is what we'll get:
As we can see, the representation is correct and George is the most diligent one. We can also see that John is not at all in the middle, but is almost as diligent as George.
So, the L value only shows us the number of apples left in each box, while the F value shows us the diligence of each person.
In order to derive the L value I used subtraction, and in order to derive F I used division.
Now is the question: What if I use logarithms ($X = \log_T O$), what will the derived values X will represent then?
