Hello Salahuddin, this was part of a question that my student asked me some time ago. He was not familiar why log should be used at all. Log is often used in population curves. On the y axis, we have 1, 10, 100, 1000, and we have a nice hyperbola. The good thing is that it's easy to remember, at least for my student.
So I explained from a simple cell division process: 1 cell, 2, 4, 8, 16, 32 (also a log pattern). Very often in reproduction and growth, we meet up with log curves. Have a good day.
There is lots of online support on the question of data transformation...and much has been written on log transformation and the topic of data transformation in general (just "Google" it).
Briefly, log transformation is used for many purposes, but is especially popular when data are skewed right. In such cases, log transformation will make the distribution more symmetric and "normal". Hence, it is often used to transform data to meet the assumption of normality in an inferential test (that assumes the data are normally distributed). As shown above, it is also a convenient way to make a linear relationship between a dependent and independent variable more visible.
If you are interested in -fold (or percentage) differences in a variable than use log transformation. For example, with the base 10 logarithm: numbers 10, 100 and 1000 will be equi-distant because 100 is 10 times 10, and 1000 is 10 times 100. Thus, logarithm gives you a better idea about the proportional differences between data points.
Besides, many phenomena scale exponentially (e.g., stock market mania and stock market collapse) . . . and log transformation can be used to demonstrate to some stubborn 'non-believers' that share price can drop 50% infinite number of times (or until the stock is delisted from the stock exchange).