No, log transformations are not necessary for independent variables.  In any regression model, there is no assumption about the distribution shape of the independent variables, just the dependent variable.

In particular, when using logistic regression, the interpretation of the odds ratio will be a per-unit change of the independent variable so a log transformed variable would difficult to interpret (i.e., for each additional log-unit of x the risk of y...).

I hope this is helpful!

Mike

Thanks Mike for the reassurance.

Principally even in situation where transformation is necessary  independent variables are not transformed in neither OLS nor logistic regression. While transformation applies only to Dependent variables in the case of OLS you should also remember that  we go for logistic regression among other reasons when our data fail to comply with the assumption of normality. For this reason definitely transformation not necessary for your case. 

Thanks Stephen, Kenneth 

 No. you are not in need for doing any log transformation for that.

Thanks Alyaa.

Just curious...you don't have to perform a log transformation, but is there ever a time when one should? For example, I have a very positively skewed, continuous independent variable (number of on-campus work hours for 553 students). It was one of several variables used to predict whether a graduate was employed full-time or less than full-time. The result: B = .001 and an odds ratio of 1.001. The p-value was 0.13. Does this mean that work hours has no effect and that this result is significant at p < .05? Should I transform this variable or just accept the result? I ran the same model using subsets of the data (non-white graduates, low-EFC grads, humanities majors, etc) and in every single case the B and odds ratio values are the same (although the p value changes some). Oh...I'm no expert. Just trying to finish a dissertation. Thanks.

Thank you all for useful comments.

But I have a question...

if the coefficients in the Binary Dependent Variable regression were insignificant, what shall I do? can I still interpret the coefficients ?

What ordinal level DVs and IVs? Can they be log transformed?

If your data are clustered near floor or ceiling, then you should do a logistic transformation to even be able to run an ANOVA--but it doesn't fully solve the problem of such data, it just artificially forces it into what looks like a normal distribution.