How should I store a log for my plugin

It is not clear exactly what you are doing. For example, I am not sure what the data is that you are saving or where/when it needs to be displayed, but it sounds like you need:

  1. The Transients API
  2. Or the Options API

However, if your data is very complicated you might want a dedicated table. Without more information, that is the best I’ve got.

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