Product label font question

have a logo with a slogan for a cosmetic brand I’m working on, but when the label is scaled down for smaller cosmetic container the slogan isn’t clear.

Do I change the slogan font size on smaller bottles, but this could overtake the main logo font?

Or do I change the font type in the hopes that the slogan will be more visible when applied to smaller bottles?

The logo and the slogan are separate design elements. Treat them separately. Make it work.