The mkmf.log file can be found under the gem’s installation directory.
rvm
If you are using RVM, then look for a directory similar to
~/.rvm/gems/ruby-1.9.3-p194/gems/some-cool-gem-name/ext/mkmf.log
You can list all the mkmf.log files available with this command:
find ~/.rvm -name mkmf.log
rbenv
find ~/.rbenv -name mkmf.log