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Home » Find the value of \( x \) in the equation \( 2^x = 64 \). - Parker Core Knowledge

Find the value of \( x \) in the equation \( 2^x = 64 \). - Parker Core Knowledge

📅 May 5, 2026 👤 scraface

May 05, 2026

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Step 2: Incorporate \( N \equiv 4 \pmod{7} \)
Let \( N = 20b + 7 \). Then:
20b + 7 \equiv 4 \pmod{7} \Rightarrow 20b \equiv -3 \equiv 4 \pmod{7}
Since \( 20 \equiv 6 \equiv -1 \pmod{7} \), we have:
b \equiv 4 \pmod{7} \Rightarrow b \equiv -4 \equiv 3 \pmod{7}
So \( b = 7c + 3 \), then:
N = 20(7c + 3) + 7 = 140c + 60 + 7 = 140c + 67
Smallest positive \( N \) when \( c = 0 \): \( N = 67 \)
Check all conditions:
\( 67 \div 4 = 16 \times 4 = 64 \), remainder 3 → ✓

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