I thought LimeSurvey keeps a log for the time for each survey taking and the date. but its not
Limesurvey does, but only if you tell it to. As this information can be relevant for data protection, it is default to not recording it, if you don't specifically configure it.
Before activating a survey, Limesurvey is quite explicit on this and gives a big warning/information sign:
You can only set this, when the survey is not active. So you either deactivate the surveys and on re-activating make these settings or you will have to live without this feature for these surveys.
Help us to help you!
Provide your LS version and where it is installed (own server, uni/employer, SaaS hosting, etc.).
Always provide a LSS file (not LSQ or LSG).
Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.