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Home » Solution: The square root of a square simplifies to the absolute value: - NBX Soluciones

Solution: The square root of a square simplifies to the absolute value: - NBX Soluciones

📅 May 3, 2026 👤 scraface

May 03, 2026

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Find the value of \( x \) that satisfies \( \log_2(x^2 - 4) = 3 \).
Start by rewriting the logarithmic equation in exponential form:
\[ \log_2(x^2 - 4) = 3 \Rightarrow x^2 - 4 = 2^3 = 8. \]
Solve for \( x^2 \):
\[ x^2 = 8 + 4 = 12 \Rightarrow x = \pm \sqrt{12} = \pm 2\sqrt{3}. \]
Since the argument of a logarithm must be positive and \( x^2 - 4 = 8...
Thus, one solution is \( \boxed{2\sqrt{3}} \).
Clarification Note:** Since \( \log_2(x^2 - 4) = 3 \) requires \( x^2...
\boxed{2\sqrt{3}}
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