How can we Zip multiple files created on the same date into one single zip file.?

Hi all i am very new to shell scripting and need some help from you to learn
1)i have some log files that gets generated on daily basis example: i have abc_2017_01_30_1.log ,2017_01_30_2.log like wise so i want to zip this 4 logs which are created on same date into one zip folder.
2)Post zipping i want to delete the individual files and keep the zipped folder .
3)i want to delete the zipped folder which are older than three days.
I was able two achieve 2 and 3 but failed to get the first step please suggest me any methods it would be helpful. Thanks

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