Log of dummies variables
A dummy variable is a binary variable, that does need to be logged. You can use them as they are. Also, if the variable is set to 1 for a given result and zero otherwise, by taking logs you will turn your variable to 0 and a missing value because the log of 0 does not exist.



update: Instead of a plot, why not simply calculate pairwise correlation coefficients. Here is an example using Stata

. sysuse auto, clear
(1978 Automobile Data)

. * Create a dummy variable
. gen byte big= weight&gt;3020

. ta big

        big |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         35       47.30       47.30
          1 |         39       52.70      100.00
------------+-----------------------------------
      Total |         74      100.00

. * Correlate big with price
. pwcorr big price

             |      big    price
-------------+------------------
         big |   1.0000 
       price |   0.3469   1.0000 

Both are positively correlated.

. * Add a other dummy and compute new correlations


    pwcorr price foreign big

             |    price  foreign      big
-------------+---------------------------
       price |   1.0000 
     foreign |   0.0487   1.0000 
         big |   0.3469  -0.5682   1.0000