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📅 May 4, 2026 👤 scraface

May 04, 2026

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Thus, the value of \( a \) is \( \boxed{\frac{20}{7}} \).
Rationalize the denominator of \( \frac{4}{\sqrt{5} - \sqrt{3}} \).
To rationalize the denominator, multiply numerator and denominator by...
\frac{4}{\sqrt{5} - \sqrt{3}} \cdot \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5...
Thus, the rationalized expression is \( \boxed{2(\sqrt{5} + \sqrt{3})}...
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 \( x^2 \):
\[ x^2 = 8 + 4 = 12 \Rightarrow x = \pm \sqrt{12} = \pm 2\sqrt{3}. \]

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