logs should be in text. The last thing you want is to find out that your binary format cannot be decoded due to a bug in the logging or because file got corrupted. Not to mention that you won't be able to integrate with a lot of log systems like Splunk and friends.

On the other hand, if you have logs, you need to store them in a centralized place and have an aging policy, etc... Grepping is definitely not the answer. Systems like Splunk exist for a reason.