Marinada '22

[lang=hr] Kažemo da je niz brojeva $x_1, x_2,\dots $ \textit{geometrijski} ako postoje brojevi $x$ i $q$ takvi da je $x_1 = x$ i za svaki sljedeći član niza vrijedi $x_{n + 1} = x_n \cdot q$. Koliko ima parova prirodnih brojeva $(x, q)$ koji zadovoljavaju $$\log_8 x_1 + \log_8 x_2 + \dots + \log_8 x_{12} = 2006?$$ [/lang] \\ \\ [lang=en] A sequence of numbers $x_1, x_2,\dots $ is called \textit{geometric} if one can find numbers $x$ and $q$ such that $x_1 = x$ and every other term satisfies the condition $x_{n + 1} = x_n \cdot q$. How many ordered pairs $(x, q)$ of positive integers are there that satisfy the equation $$\log_8 x_1 + \log_8 x_2 + \dots + \log_8 x_{12} = 2006?$$ [/lang]