MathNet 2008-part-03 — 165 problems (EN–VI) Question 142

In the product of powers $5^{-2} \cdot 5^{-4} \cdot 5^{-8} \cdot \ldots \cdot 5^{-x}$, where the exponents form a geometric sequence, determine $x$ so that $5^{-2} \cdot 5^{-4} \cdot 5^{-8} \cdot \ldots \cdot 5^{-x}=5^{-16382}$.