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Problem 249

AMC 10/12, early questions

Algebra Difficulty 3.9 Find the answer Harvard-MIT November Tournament · United States

Problem:

Let $x$ be a real number such that $2^{x} = 3$ . Determine the value of $4^{3x+2}$ .

Your answer

Official solution

Solution:

We have
$4^{3x+2} = 4^{3x} \cdot 4^{2} = \left(2^{2}\right)^{3x} \cdot 16 = 2^{6x} \cdot 16 = \left(2^{x}\right)^{6} \cdot 16 = 3^{6} \cdot 16 = 11664$

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