Clear Log Module Configurations:
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The Clear Log  module provide option for number of  days in Logging and errors interface to delete the Recent Log Messages for specified number of days, on Cron Run

Recent Logs Messages will be deleted for specified number of days, on Cron Run

Site should Database Logging Module Enabled

The module provides a drop down in Logging and errors where we can select number of days to keep log messages.

We can implement hook_days_limit_settings_alter to change the drop down options

Example to implement days_limit_settings_alter 
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function {moduel_name}_days_limit_settings_alter(&$options) {
  //Change Options data.
}