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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 $. 📰 The 1 Online Brokerage Proven To Boost Your Investmentsdont Miss Out 8756910 📰 Game Changer Inside The Mystical Gme Message Board Thats Taking Over Forums 9037345 📰 Supplications 6770013 📰 Roblox Giftcard Digital 4804208 📰 Football Player Roger Staubach 9310165 📰 5 Death Note Movie The Hidden Truth That Will Scare You Off Forever 7173035 📰 Case 2 1 Red 2 Green 1 Blue 3732696 📰 You Wont Believe This Dvd Player Software Can Restore Your Old Movies Instantly 723555 📰 Pins Stock Price 7630164 📰 Random Questions To Ask People 209532 📰 Sarah Palin Stuns In Red Bikini The Bold Look That Set Headlines Firing 9058171 📰 Sparkling Accuracy How To Spell Miscellaneous Like A Pro In Seconds 9088725 📰 Rachel Boston 2836422 📰 Paul Mescal Height 514936 📰 Shocking Gift Ideas For Book Lovers You Need To See Now 67866