Here is the Log of History for January 6, the 6th day of the year.
1000*Log10(6) = c.778 because 10^0.778 = c. 6.
So, what happened in the year 778 A.D.?
Not a whole lot that I can tell.
A minor ambush turns into a major legend: In 778, Charlemagne was retreating from an unsuccessful invasion attempt. He ordered Roland to guard his rear at the pass of Roncesvalles from a potential major attack on his army. Instead of a muslim attack, however, Roland fell to a surprise attack by a Basque force. Legend has it he blew his famous horn too late to summon Charlemagne to help.
Over to the East, in the as-yet-unconquered Roman Empire, Emperor Leo IV repulses a muslim invasion in Germanicia, not that it did much good. That area changed hands quite a lot. Leo IV has no particular fame in Roman history other than being married to Irene, who became Empress once he died. Irene had secretly undermined the religious policies of Leo IV during his lifetime, and once he died spread the story that he had committed sacrilege and so died as punishment. There was some diplomatic talk about the possibility of reuniting the Roman Empire by having Charlemagne marry Irene, but nothing came of it in the end.
Ahmad Ibn Hambal ash-Shaybaanee, an important Islamic scholar, is born in Baghdad in 778.
"The number of foot-pounds of mechanical energy equivalent to one British thermal unit is called the mechanical equivalent of heat, and equals 778 foot-pounds". Huh. Who'd a' thunk it?
The Log of History so far:
1000xLog(1) = 0 Jesus' Birth.
1000xLog(2) = c.301 Armenia becomes Christian; Diocletian fixes prices.
1000xLog(3) = c.477 Zeno informed Rome no longer has an emperor; Shaolin Temple built.
1000xLog(4) = c.602 First Anglo-Saxon laws recorded; Byzantine Emperor Maurice murdered.
1000xLog(5) = c.699 Beginning of Salzburg; Hanifa founder born.
1000xLog(6) = c.778 Battle of Roncesvalles; battle of Germanicia.