I'm trying to come up with decent populations for my settlements, mainly. My homebrew setting was classic fantasy, similar to Faerun, but then there was an industrial revolution 30 years ago. Now it's more steampunk, though there is still plenty of magic. What would you think the populations are like? For the capital, a small farming town, a logging town, a mining town? Any insight would be appreciated, thank you!

DO NOTE, ALL NUMBERS I SAY IN THESE PARAGRAPHS ARE FOR THE SMALLEST SIZE OUTPOST, TOWN, OR VILLAGE! 

well, for the capital, that would depend on the type of government. but for the most part, it would be about an even mix of high class officials and rich merchants/craftsmen (such as jewelers, and tailors that sell directly to the rich people, and also tinkers that specialize in the hard-to-make clockwork and steam-powered machines, such as clocks and miniaturized ion power packs, and of course you can't forget the magicians that sell high-grade enchantements); middle class merchants and specialist crafters that make things that are hard to mass produce, but don't sell for a fortune; and then finally would be your lower class people, such as your general laborers, orphans, poor people, and the homeless that can barely feed themselves, with the homeless and orphans most likely being more proliferant, since with the industrial revolution happening only 30 years ago, people should still be getting used to the new technology level, and there will be an increase of fatal accidents on the job from either not enough knowledge or just machine failure, which would increase the number of orphans, and then the increase in mechanized work will increase the homeless because it would put people out of jobs. Total Population- about 25,000 people at most that live in the city. if you take into account travelers, merchant caravans, visitors, and adventurers, i'd say about 100,000 people total.

A small farming town in a fantasy world that is developing technology at a rapid pace would mostly stay the same, except that they would be cleaner, have more clothes that are a better quality, and have access to more common iron objects at a cheaper price. Any smiths that are in the towns might have upgraded to a blast furnace, with several molds so that he can cast-forge items such as horseshoes, pots, pans, and various cutlery. The farmers themselves wouldn't change much, unless they are the rich kind, then they might have a machine or two that would help with the planting or harvesting, or even both. I'm not sure what else i could tell you about a farming town, since i've never really been to one or researched them. Total population- at most 1000 people for the biggest farming village, while the least would be 200 people

so, for a logging town, the main population would be your laborers, in particular woodcutters. they would take up about 64-75% of the population(which could go from about 25ish people to over 100, depending on the size of the outpost). Their sleeping quarters would be either a tent city, or wooden dorms that have 4 men to a room in bunk beds, with a common area, a small cafeteria that has , and a storage area for any excess equipment(this would depend on if they were hired by a company that sent them there, or if they work for the lumberyard as woodcutters. you could add both the dorms and the tent city if you feel it necessary.) . Then you would have an innkeeper for the more well-to-do travelers that have a bit of money to spare, and he would have up to 3 cooks, one of which would be his wife, and have up to 7 waitresses, depending on the size of the town, the size of the inn, and how often travelers come through.  There would also be a stable that has about 20 horses (workhorses to be exact, along the lines of a clydesdale), with a storage barn nearby that has 10 wagons capable of hauling logs. Manning the stables and barn would be 5 stablehands, with a stable master overlooking them and the barn, and you'd need 15 cart drivers, with 1 for each wagon while having 5 in reserve, for shifts. There would be a general store, which would have about 4 or 5 clerks, in addition to the guy in charge, with only half of the clerks working at a time. you would need a lumber mill, who's design would change depending on the region. (if there's a river or large stream, it would be powered by a waterwheel, while in a windy area it would be powered by a windmill. Or you could come up with some kind of mechanical solution to that problem, such as using some kind of crystallized magic, or stored kinetic energy from a spring). This lumberyard would have 10-15 workers, along with a foreman, and a smith/tinker who would be in charge of making any repairs to the saws, along with making new parts when necessary. Then you would have the guy in charge of the whole place, who could be either a representative of a merchant guild that specializes in wood, a disgraced noble sent here by his father or mother to learn some responsibility, or an entrepreneur who is payed to get the town/outpost started up, which makes everything his property. Though, the people working in the lumberyard will most likely either be working for him or for a merchant guild. total population- between 50 (the minimum number needed for a small outpost to run smoothly) and 500

For the mining town, it would be pretty similar in composition to the logging town, except you would have a depository for the ore instead of a lumber yard, and you would only have 5 wagons and 10 horses and 10 drivers (these will be for transporting the ore to a nearby city after enough has been collected, or they would transport ingots if you have a blast furnace on site). You could also have about 10 donkeys, for pulling mine carts in the tunnels, if its a bigger operation). Next to the mine entrance there would be a smithy, which would have between 2-5 smiths on site at all times during working hours to repair picks and shovels as needed. There may also be a cafeteria with 5 cooks running the tray line. The total number of miners would be between 27 and 100, depending on how deep the mine is, how wide the tunnels are, what type of ore there is inside, and a few other things. Total population - between 100 and 700

So, i hope you find this little infodump to be useful to yourself sir, and would like to make a note- in a post-industrial revolution world that has magic, most of the factories that pop up would start developing ways for the machinery they use to take advantage of any mana in the air or that in inserted into a mana gem or something like that, which would make magicians and spellcasters in general rise in value, so you could include a Mage Academy City. For a medium sized city, you would have the instructors, which would be about 15% of the population. Then you would have the general staff, who would take care of the dorms, general cleaning, maintenance, and stuff like that. they would account for 25% of the population. Then you would have the students, who would take 35-40% of the population, with them being split by how many years they've been at the academy. Then you would have the administration. This would be the Headmaster, people in charge of admissions,the people in charge of classes, and so on and so forth. This would be another 5% of the population. and finally you would have the people that live in the city because they have businesses, such as shopkeepers, crafters that focus on things that student mages would need, and several inns. This would be the last  15% of the population. Just think of it as a city-sized college. The students would be put in dorms based on either what years they are in, or on their level of wealths, with the separations being based on housing districts. (district 1, district 2, and so on). There could also be an arena where you could hold tournaments, which would require the administration staff to be increased to 10% and the students to be reduced to 35%. There would be either restaurants out in the city, or cafeteria's in the academy limits. and i can't think of anything else for this academy city. well anyways... Total population- 10,000-25,000

Have fun sorting through this info, and good luck with your group!

HOLY CRAP. Thank you so much!! This is incredibly helpful, you have no idea. I was super low in my estimates. I'm blown away, thank you again! :)

not a problem. also, with the minging and logging town, anything smaller than that will be known as an outpost. also, i hope you put this info to good use. i was happy to help

So, how did this go with my info?

That was 8 years ago - they may not even be around any more let alone remember how the world building went. Some real world data  and comments below.
1) capitols - yes lots wealthy and powerful but about half ( or more) of  the population would actually be servants and support staff. And the range in sizes is huge, taking 1880 as a good point roughly 30 years after the British & American industrial revolutions start ( based on the invention of steam railroads in the 1840s), the population of Denver, CO was @35,000, Washington DC was @170,000 and London, England was @ 3,000,000. 
2) logging and mining ( especially) tend to undergo a boom and bust pattern so populations change up ad down rapidly. Virginia City, NV is a good example. In 1850 it was a small mining village with a population probably below 1000 ( actually unrecorded). Then in 1859 the comstock load was discovered. By 1860 the population was @2300, by 1874 it had reached 25,000 and, with the mines starting to play out, by 1880 it was down to @10,000. By 1900, with the mines pretty well played out, it was back down to @2500. Portland OR provides a different view showing what diversification of industry can do. In 1860 it had a population of @2800. The introduction of a steam shipping company provided a means of export ( and import) for regional products caused the city to grow to @30,000 by 1870. The addition of railways connecting the city to mines, timber areas, farming and fishing areas in the 1870s caused further growth. By 1880 the population was @58,000 and by 1900 it was @90,000.
3) magic would have changed the way many things were done. A real blast furnace needs iron ore, coke or charcoal, and limestone  at a minimum. The burning coke heats the ore and limestone  causing the ore and limestone to melt with the carbon gases reacting with the iron oxides reducing them to pure iron with an admixture of carbon (roughly 3% for most “pig” iron). The limestone reacts with the waste minerals in the ore creating a light slag that floats on top of the molten iron. The molten iron is poured off into molds called “pigs”  and sold. Blacksmiths buy the iron and work it further. With magic you still need the same things but your blast furnace might have a fire elemental embedded in ti as the heat source so you would need less coke/charcoal. But if you don’t have ready access to the raw materials - in large quantities - there is really no point or way to make a blast furnace. Most blacksmiths would never have one for this reason. They need a source for the iron and coke/charcoal for their forges  but those can come in from elsewhere via transport systems cheaper and easier than doing it all themselves. So iron (and later steel) production would, as it was in the US, Britain and Germany, be centered on regions with easy access to the three raw materials and the finished iron (and later steel) would be exported from there to local black smiths. At these centers magic in the form of summoned elementals etc would be very useful, at the level of the village blacksmith much less so. Steel making actually reduces the carbon content of the iron to anywhere from 0.5 to 1.5% depending on the type of steel you want. 
4. what makes for an Industrial Revolution isn’t so much the industry as the development of an effective “high speed” transport network that allows you to concentrate resources conviently for the industry.