I process "3x cheaper" as "for the same money, I can get 3x the original amount".
Which would be 33% the original price.
Which would be 33% the original price.
For the opposite word, "expensive", it all depends on the word before it: "as expensive" or "more expensive".
"100 widgets cost $100. Unit price is $1." They are now twice _as_ expensive -> they now cost $200. Unit price is now $2.
"100 widgets cost $100. Unit price is $1." They are now two times _more_ expensive -> they now cost $300. Unit price is now $3.
But How do you do this with the word "cheap"? Does "cheaper" clearly mean "3x as cheap" or "3x more cheap" (which even sounds a bit wrong)? I guess it means "more cheap" means "cheaper".
Better to avoid the problem and say "They are now two times the cost, or half the cost". Which is much clearer.
Frustratingly, I find this isn't always true in practice. Lots of people use "x times as y" and "x times more y" interchangeably. To avoid ambiguity I try to only use the former in any context where precision is useful.
It’s also used more generally for buy one get one X% off sales and you’ll see lots of “BOGO50” promo/coupon codes. Then marketing jumped on the bandwagon and started plastering “BOGO” all over marketing material so consumers are used to the lingo now