Found on The Island by Nathan Drake and Elena Fisher, the log book of the Lost Colony contained key information regarding the arrival of El Dorado to the colony. Also, the customs house in which the log book was found was also a major discovery for Fisher and Drake as it contained all the ship manifests and logbooks for the entire colony, a major historical find to lend archival evidence to the "Lost Colony".
Upon arrival at the customs house, Nathan Drake discovered the log book lying open on the table. Upon closer inspection, he discovered the name of the ship which brought El Dorado to the island, the Esperanza. Nathan Drake, showing great ability at reading the 16th Century Spanish in which the book was written, discovered the vast treasure the ship had been carrying along with the statue weighing in at "20 arrobas" (equivalent to exactly 500lbs). Turning the page, Drake discovered the illustration made by one of the custom house officials of El Dorado shortly after it's arrival at the colony. However, despite this discovery Drake was focusing more on leaving the island and took the page with the drawing but stated that it would be the closest they came to El Dorado. Before they could depart the island however, the arrival of supposedly dead Victor Sullivan convinced Nate to remain, much to Elena's delight.