Varnish, by default, doesn't write a lof file. If you go to /var/log/varnish you will see that this directory is empty.
In Magento, using the Turpentine module, you can enable Varnish logging but it writes a *ton* of stuff and is very heavy to work with. It also degrades server performance asd fills storage.
You can monitor Varnish by typing
varnishlog but you will get flooded with information. There are a multitude of switches available, just see
man varnishlog. Even still, this log can be a lot to handle.
varnishncsa instead. It will give you a "tail-like" experience minus all the cruft. You can actually watch this monitor and get a good sense of what's happening in your mail server without trying to filter all the noise.