For me, I tend to think of "3x" and "cheaper" as separate operations. So "3x cheaper" sounds like you're saying new_price = price - 3*price.

That (usually) makes no sense, so I assume people mean something else when they say it, but I never have any clue what. Is it a third of the original price? Is it two thirds (new_price = price - price/3)?

Percentages also work this way. If I say "10% cheaper", most people understand that I mean the price is 90% of what it was previously. Although percentages get weird when increasing the price.

e.g. if it was a flat doubling, I would say that as "200% of the price" (new_price = price*(200/100)).

However, I take "200% more expensive" to mean new_price = price + price*(200/100). To me, the "more" implies addition specifically.