You'll see that any transactions you make that modify your credit balance will be shown here.
This includes buying credits, gifts, giftpapers, products, or selling products, or sending credits.
Because your log might be overflowing with items, be sure to make use of the begin and end date boxes if you're looking for something specific.
If you're looking for proof that a reseller sent you credits, this is a great place to look.
When you buy credits from a reseller, you will NOT receive an email from IMVU announcing the incoming credits.
Some resellers send emails with credit purchases, but that varies among resellers.
In your log, any credits sent to you by a reseller will have an entry with the "reason" column starting with giveCreditsAndProducts:credit.
Then in parenthesis will be a unique number set by the reseller. The user number at the very end is the ID number of the avatar that sent the credits.
In this example, 5000 credits were given by user 25298318, which is the number of EvilCredits.