We use the log of the variables to have comparable dimensions. When the log of the variables are not stationary and they are integrated of order one; we use their first differences which represent their growth rates.

Dear Naveed,

Another reason why variables are transformed is to make the relationship between them satisfy the assumptions of linear regression. This is best viewed through the dispersion pattern of a scatter plot, which should be "cigar shaped".

Use of log makes the non-linear growth function linear. This transformation makes the further calculations like parameter estimation, parameter identification etc.,  easier and simpler. The tools of parameter estimation for the non-linear regression model are more difficult to be applied than those for the linear regression model. Without this transformation, the parameter optimization becomes cumbersome, problematic and ill-posed problem. It is to be noted that every non-linear problem can be transformed to a linear one.

Thank All and  especially Patrick S Malone sir 

 A transformation variable is to pull outlying data from a positively skewed distribution closer to the bulk of the data in a quest to have the variable be normally distributed.(see Introductory Econometrics: A Modern Approach by Woolridge for discussion and derivation).

But in the case of GDP per capita in constant dollars, the transformation in log differences can be assume as a measure that is comparable across countries?