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The audit log of JIRA Application does not track any kind of issue/ticket update activities, as you can see in the Audit Log documentation:
The audit log isn't intended to record all activity in Jira. For example, it doesn't track issue updates or pages that are viewed by a user. The audit log is intended to record configuration changes that can impact users and projects.
For issue update activities, I recommend you use the activity stream gadget that provides you with all the activities performed in the tickets you want, including any changes applied to their descriptions.
To know how you can add the Active Stream Gadget and add a filter to refine your searches on it, you can check the documentation below:
Let us know if you have any questions.
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