Can make use of docker logging features by symlinking log files to /dev/stdout and /dev/stderr. E.g.:
RUN ln -sf /dev/stdout /var/log/nginx/access.log &&\
&& ln -sf /dev/stderr /var/log/nginx/error.log
This is also another metric for whether your containers are too complex -- symlinking one file to stdout and the error log to stderr should be enough to keep track of how your container is doing.