1000xLog10(3) = c.477 because 10^0.477 = c. 3.
So, what happened in the year 477 A.D.?
According to this website, there was a ruler in India named Buddhagupta. That should be an easy one to remember, although I have no idea of his significance in Indian history. (Just in case you're curious about the relation to the Buddha, Siddhartha Gautama, there was at least one scholar who calculated the Buddha's death to 477 B.C. See page 22 of the linked book. Of course, that's 477 B.C., not A.D.)
Aelle, Chief of the Saxons, founded the Kingdom of Sussex in southern England. I wonder if this is what the Anglo-Saxon Chronicle was referring to in the entry for the year 477: "This year came Ella to Britain, with his three sons, Cymen, and Wlenking, and Cissa, in three ships; landing at a place that is called Cymenshore. There they slew many of the Welsh; and some in flight they drove into the wood that is called Andred'sley."
In the Roman Empire, 476 is a much more significant year: it was the year that Odoacer conquered Rome and began to act as king over Italy. He apparently didn't have much use for the pretension that the Western Roman Empire had anything in the way of a real emperor. He forced the previous Western emperor to resign. It was in 477 that he had the Senate send a letter to the Eastern Roman Emperor Zeno saying saying they were okay with just having one emperor, in Constantinople, and please just accept Odoacer as the wonderfully loyal guy you've put in charge in Rome. (This is from Edward Gibbon's History of the Decline and Fall of the Roman Empire, Volume 3, page 474. On page 477, I read this: "Odoacer was the first Barbarian who reigned in Italy, over a people who had once asserted their just superiority above the rest of mankind." Some attitudes never go away.)
The original Shaolin Temple was built in China in 477 A.D.
Also in China, Xiao Daocheng, later known as Emperor Gao, has a wacky encounter with the 14-year old Emperor Houfei where the violent boy tried to use his large belly for archery target practice. I know it's Wikipedia, and I generally don't like quoting Wikipedia, but this is too good a story to pass up. Xiao Daocheng rationally makes the decision to assassinate the crazy kid and replace him. So he basically starts a new dynasty in 477.
This website (as well as others) claim 477 as the birth year of Cassiodorus, who became a Benedictine monk. He is credited with believing "...that knowledge of the classics is mandatory for understanding the Bible. He also include[d] copying manuscripts as "manual labor" suitable for monks. The preservation of all classical Latin texts is due to the persistence of Benedictine monks, under the guide of Cassiodorus". Earlier in life he had been an important statesman who helped reconcile the Romans to their Germanic conquerors. A lot of what we know about how they ran things is due to his writings. The year before he was born, as noted previously, was the last year a Western Roman emperor ruled in Rome. Translations of Cassiodorus' writings can be found at gutenberg.org
An Early History of Horsemanship, p157 by Augusto Azzaroli says the first mention of stirrups in Chinese literature occurred in 477 A.D. Most websites I've read claim that stirrups were invented in China or Korea about that time, but this particular author says there is artistic images of Kushan nomads using something closely resembling stirrups from around 100 A.D. He believes stirrups were spread both east and west by nomadic migrations. Regardless of their origin, stirrups were an enormously important invention, so I think I'll include it here.
Other oddities:
Apparently the 477 nanometer wavelength is the longest wavelength still considered "blue" light. Here is a site to build a blue-wavelength light box to treat low-light induced depressions.
According to this light box manufacturer, blue light at the 477 nanometer wavelength is on the edge of the spectrum that helps people's moods. "The specific bandwidth of light that is responsible for suppressing melatonin and shifting circadian rhythms encompasses light in the range of 446 – 477nm (nanometers)".
The Log of History so far:
1000Log(1) = 0 Jesus Birth.
1000Log(2) = c.301 Armenia becomes Christian; Diocletian fixes prices.
1000*Log(3) = c.477 Zeno informed Rome no longer has an emperor; Shaolin Temple built.