Dear Mr. Young,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Logbooks of U.S. Navy Ships and Stations, 1941 - 1983 in the Records of the Bureau of Naval Personnel (Record Group 24) that include the deck log of the LST-771 for 18 October 1844 through 14 May 1946. For access to and/or copies of this log, please contact the National Archives at College Park - Textual Reference (RDT2) via email at firstname.lastname@example.org.
In addition, we searched the website of the Naval History and Heritage Command and located a brief article about LST-771.
We hope this information is helpful. Best of luck with your family research!