How to check that cron is reindex the complete site? I'm using drupal 7 and cannot find a log that the site is reindexed.

Cron is running every 3 hours which I can see in the log. How can I check that the cron is reindex my site as well?
Go to admin/config/search/settings or Configuration > Search and the top of the page will tell you how much of the site has been indexed.

The button "re-index" will let you re-index the site and the status above it will still tell you how far along the indexing process is. By default, Drupal indexes the website during cron runs and the option below the "re-index" button lets you select how many nodes are indexed per cron run.