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... I'm running ccleaner daily (or almost) and the following two files were deleted because of a rule named "chrome logs": ...
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As far as I know, CCleaner does not have a rule named "chrome logs". It seems that you are using a file for extended cleaning, like the file "winapp2.ini". You should check if there is an updated version of that file.
The issue with the cleaning rule Chrome [Logs *] should now be resolved. Now the rule only deletes usual informational logs and not important database files anymore.
(If you update the FAQ you should add the rule Chrome [Extensions Databases *], because this rule resets all extensions.)