The captain's log on the HMS Bounty was kept during the exile of Admiral Kirk and his USS Enterprise command crew on Vulcan from the end of 2285 into 2286. (Star Trek III: The Search for Spock; Star Trek IV: The Voyage Home)
The only log shown to exist was made shortly before the Bounty disembarked for Earth.
The log recordings presumably went down with the Bounty herself when she crash landed in San Francisco Bay following the return with the whales and her consequential run in with the probe. Their final fate is unknown.
- "Captain's Log, Stardate 8390. We are in the third month of our Vulcan exile. We are uncertain about the progress of Captain Spock's memory training. And it was Doctor McCoy with a fine sense of historical irony, who decided on a name for our captured Klingon vessel. And like those mutineers of 500 years ago, we too have a hard choice to make. A choice made harder because we are all too old to suffer fools gladly."