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Home » \ln(e^0.3t) = \ln(20) - Veritas Home Health

\ln(e^0.3t) = \ln(20) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Compute each term:

📌 2(3\sqrt{2})(2\sqrt{3}) = 12\sqrt{6}

📌 Final answer: $ \boxed{30 - 12\sqrt{6}} $

📌 Question: Rationalize the denominator of $ \frac{5}{\sqrt{7} + \sqrt{2}} $.

📌 Multiply numerator and denominator by the conjugate $ \sqrt{7} - \sqrt{2} $:

📌 \frac{5}{\sqrt{7} + \sqrt{2}} \cdot \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}} = \frac{5(\sqrt{7} - \sqrt{2})}{(\sqrt{7} + \sqrt{2})(\sqrt{7} - \sqrt{2})}

📌 Simplify the denominator using the difference of squares:

📌 \frac{5(\sqrt{7} - \sqrt{2})}{5} = \sqrt{7} - \sqrt{2}

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