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Home » Question: If $ 2^x \cdot 8^x-1 = 64 $, what is the value of $ x $? - Silent Sales Machine

Question: If $ 2^x \cdot 8^x-1 = 64 $, what is the value of $ x $? - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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We are given a recursive sequence:
\( a_1 = rac{1}{2} \)
\( a_{n+1} = L(a_n) = a_n - rac{a_n^3}{3} \)
We seek \( \lim_{n o \infty} a_n \), assuming the limit exists and eq...
If the limit exists, then:
L = L - rac{L^3}{3} \Rightarrow rac{L^3}{3} = 0 \Right
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