My Alchemy was level 20 and it took about ten or more potions just to level it up once.

You level up faster if you make more expensive potions. Find or make best alchemy enchantments you can. Aggressively take perks to make your potions stronger as you level up. Make most expensive types of potions. Those are: Fortify Health with Giant toe, Damage Magicka Regen, Paralysis, Invisibility, Slow, Regenerate magicka/health/stamina.

Sounds about normal.

Higher end potions level it up faster. Of course those are the ones with the ingredients that are a bit more rare and hard to find. Some of the potions will barely move your level. Those are the ones that you can pick up ingredients for by the hundreds as you walk everywhere.

So it seems that Alchemy is way different than Smithing and Enchanting.

It's actually one of the best skills made for Skyrim in my opinion.

Alchemy has always been slow, others were simply too fast.

Actually they are all the same now. The skill increase is based on price tag.

There are plenty of Blue Butterflies and Blue Mountain Flowers around Skyrim, two easily obtained ingredients, that are actually easy to remember go together when starting a new game. An easy way to make money and level up. I never found alchemy that slow since I always have plenty of ingredients collected.

Well i dont know about enchanting, but smithing recently got changed to use cost too (In a recent patch).