... I have to unpack the file of the day search inside the example file with grep or cat. ...
unzip -c
and gunzip -c
-- If you need to unzip something first to learn what you want grep for, these commands will uncompress the file and print its contents to standard out, rather than to a file. This is faster than writing the uncompressed contents to a file, gives you ability to process the event logs through a pipeline, and leaves fewer uncompressed copies of the log files lying around.