using LOG in a econometric model
The use of the natural $\log$ permits to obtain approximations of percentage changes instead of unit changes (assuming linear regression). For instance, the parameter associated with $\log$ of GDP per capita would give you the changes in education (in the unit you measured it, e.g., years) as a result of an increase of 1% in GDP per capita. Notice that if your dependent variable is also a $\log$ transformation, you'll obtain elasticities. 
To conclude, it should be straightforward for you to understand that there is no reason to apply a logarithm on unordered variables, or on binary variables. Its use on ordered variables is up to you, as the economic signification of choice of the estimates is dependent on your interests.