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📰 Solution: Combine logs: $ \log_2\left(\frac{x + 4}{x - 1}\right) = 3 $. Rewrite in exponential form: $ \frac{x + 4}{x - 1} = 2^3 = 8 $. Solve: $ x + 4 = 8x - 8 \Rightarrow -7x = -12 \Rightarrow x = \frac{12}{7} $. Verify $ x > 1 $ to ensure validity. 📰 \boxed{\dfrac{12}{7}}Question: Find all angles $ \theta \in [0^\circ, 360^\circ] $ that satisfy $ 2\cos(2\theta) + 1 = 0 $, inspired by periodic patterns in environmental data trends. 📰 Solution: Start by solving $ 2\cos(2\theta) + 1 = 0 \Rightarrow \cos(2\theta) = -\frac{1}{2} $. The general solutions for $ 2\theta $ are $ 2\theta = 120^\circ + 360^\circ k $ or $ 2\theta = 240^\circ + 360^\circ k $, where $ k \in \mathbb{Z} $. Dividing by 2, $ \theta = 60^\circ + 180^\circ k $ or $ \theta = 120^\circ + 180^\circ k $. For $ \theta \in [0^\circ, 360^\circ] $, the solutions are $ 60^\circ, 120^\circ, 240^\circ, 300^\circ $. 📰 Full Moon December 4822705 📰 How Much Is Coachella 6930769 📰 Tree Meyer Lemon 3071340 📰 Throat Hurts On One Side 5557082 📰 A Historian Is Cataloging 6 Unique Historical Documents Into 2 Indistinguishable Archival Boxes In How Many Distinct Ways Can This Be Done 1781739 📰 Ash Trevino Eyelash Salon 7278050 📰 4 From Confusion To Confidence Master Line Numbers With These Simple Tricks 4036629 📰 How Many Seasons Of Peaky Blinders 7771158 📰 Miller Pony Bottles 1021228 📰 Your Next Financial Breakthrough Starts Herethe Yahoo Finance Game You Cannot Ignore 1561318 📰 Can Kara Supergirl Save The Day This Cnc Breakthrough Will Blow Your Mind 6312152 📰 Headache From Coughing 6362699 📰 2 1 2 Men 8229931 📰 Shockedravings The Ultimate World Guesser Reveals Earths Most Hidden Secret 1278099 📰 The Horry County Horror Whats Really Going On At The Schools 3689765