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Home » years = 54 months → \( 54 / 18 = 3 \) doubling periods. - Midis

years = 54 months → \( 54 / 18 = 3 \) doubling periods. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Question: If $ 2^{x} \cdot 8^{x-1} = 64 $, what is the value of $ x $?
First, express all terms with base 2:
= 2^3, \quad 64 = 2^6
2^x \cdot (2^3)^{x-1} = 2^6
\Rightarrow 2^x \cdot 2^{3(x-1)} = 2^6
\Rightarrow 2^{x + 3x - 3} = 2^6
\Rightarrow 2^{4x - 3} = 2^6
Equate exponents:
4x - 3 = 6 \Rightarrow 4x = 9 \Rightarrow x = rac{9}{4}
Thus, the value is $ oxed{rac{9}{4}} $.

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