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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 $. 📰 Verizon Wireless Monroe Street 📰 Azure Expert Managed Service Provider 📰 Family Guy Funniest Season 📰 How To Enable Steam Overlay 📰 Keyfreeze Download 📰 What Was The Lottery Numbers For The Powerball 7776401 📰 How To Extract Rar Files On Mac 📰 Rebel Dog Coffee Co 3492393 📰 Best Credit Cards Small Businesses 9372207 📰 Dog Breed Identifier 📰 2 Players Steam Games 📰 Calculator Auto 6167308 📰 Neon Shirt 1285195 📰 Con El Camino La Nueva Longitud Es 20 4 24 Metros Y El Ancho Es 15 4 19 Metros 8100766 📰 Onedrive Document Sharing 2019469