Etymology
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logged (adj.)
c. 1820, "reduced to the condition of a log" (n.1), which was old sailors' slang for an incapacitated wooden ship; thus "inert in the water."
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logon 
in computer sense, as one word, by 1975, from log (v.2) + on (adv.).
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log-rolling (n.)

also logrolling, in the legislative vote-trading sense, "mutual aid given in carrying out several schemes or gaining individual ends," 1823, American English, from the notion of neighbors on the frontier joining forces for rolling logs into heaps after the trees have been felled to clear the land (as in phrase you roll my log and I'll roll yours); see log (n.1) + verbal noun from roll (v.). "Sometimes many neighbors were invited to assist, and a merrymaking followed. [Century Dictionary]. In lumbering, in reference to rolling logs into a stream where they bound together and floated down to the mills.

LOG-ROLLING. 1. In the lumber regions of Maine it is customary for men of different logging camps to appoint days for helping each other in rolling the logs to the river, after they are felled and trimmed — this rolling being about the hardest work incident to the business. Thus the men of three or four camps will unite, say on Monday, to roll for camp No. 1, — on Tuesday for camp No. 2, — on Wednesday for camp No. 3, — and so on, through the whole number of camps within convenient distance of each other. [Bartlett]

However the phrase is not attested in any literal sense, only the political sense, until 1848.

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backlog (n.)
also back-log, 1680s, "large log placed at the back of a fire" to keep the blaze going and concentrate the heat; see back (adj.) + log (n.1). Figurative sense of "something stored up for later use" is first attested 1883, but this and the meaning "arrears of unfulfilled orders" (1932) might be from, or suggested by, log (n.2).
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log-roll (v.)
also logroll, 1835, a back-formation from log-rolling.
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blog (n.)

"online journal," 1998, short for weblog (which is attested from 1993 but in the sense "file containing a detailed record of each request received by a web server"), from (World Wide) Web (n.) + log (n.2). Joe Bloggs (c. 1969) was British slang for "any hypothetical person" (compare U.S. equivalent Joe Blow); earlier blog meant "a servant boy" in one of the college houses (c. 1860, see Partridge, who describes this use as a "perversion of bloke"), and, as a verb, "to defeat" in schoolboy slang. The Blogger online publishing service was launched in 1999.

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waterlogged (adj.)

1759 (in an account of the Battle of Lagos in "Universal Magazine," September), from water (n.1) + log (n.1); the notion apparently is of "reduce to a log-like condition." Compare logged.

WATER LOGGED, the state of a ship when, by receiving a great quantity of water into her hold, by leaking, &c., she has become heavy and inactive upon the sea, so as to yield without resistance to the efforts of every wave rushing over her decks. As, in this dangerous situation, the center of gravity is no longer fixed, but fluctuating from place to place, the stability of the ship is utterly lost. She is therefore almost totally deprived of the use of her sails, which would operate to overset her, or press the head under water. Hence there is no resource for the crew, except to free her by the pumps, or to abandon her by the boats as soon as possible. [William Falconer, "An Universal Dictionary of the Marine," London, 1784]

The verb waterlog (1779) appears to be a back-formation.

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knot (n.)

Old English cnotta "intertwining of ropes, cords, etc.," from Proto-Germanic *knuttan- (source also of Low German knütte, Old Frisian knotta "knot," Dutch knot, Old High German knoto, German Knoten, perhaps also Old Norse knutr "knot, knob"). For pronunciation, see kn-.

Figurative sense of "difficult problem, a perplexity" was in Old English (compare Gordian knot). Symbolic of the bond of wedlock from early 13c. As an ornament of dress, first attested c. 1400. Meaning "thickened part or protuberance on tissue of a plant" is from late 14c. As "small group or cluster of persons" late 14c.

The nautical unit of measure of speed (1630s) is from the practice of attaching knotted string to the log line at equal distances (see log (n.2)). The ship's speed can be measured by the number of knots that play out while the sand glass is running.

The distance between the knots on the log-line should contain 1/120 of a mile, supposing the glass to run exactly half a minute. [Jorge Juan and Antonio de Ulloa, "A Voyage to South America" 1760]

Hence the word knot came also to be used as the equivalent of a nautical mile (in pre-World War II use in U.S. and Britain, about 6,080 feet). A speed of 10 knots will cover ten nautical miles in an hour (equivalent to a land speed of about 11.5 mph).

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login (n.)
in the computer sense, as one word, by 1983, from the verbal phrase; see log in.
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logy (adj.)
also loggy, "dull and heavy," 1847, American English, perhaps from Dutch log "heavy, dull" + -y (2); compare Middle Low German luggich "sleepy, sluggish." Or perhaps a variant of loggy.
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