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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 $. 📰 Hatch Cantina 4773494 📰 Logo Maker Free Online 4586547 📰 Growagarden 252834 2238651 📰 Lifetime Smiles Start Here Discover Affordable Dental Insurance On The Marketplace 755180 📰 Cialdini Psychology Of Influence 6789042 📰 Limit Your Search Classic 1964 Chevy Impala Cars For Sale Perfect For Fans Investors 7741676 📰 Wells Fargo Bank Deer Park Tx 1653582 📰 Beware Tomate De Arbol Is Just As Powerful As It Looks Heres Why You Were Wrong About It 9825345 📰 This Simple Crontab Format Reveals How To Automate Tasks Like A Pro 6125629 📰 The Howe Daily Kitchen Bar Minneapolis Mn 8585421 📰 Geared Up For Glory Gear War 4 Shatters Expectations Dont Miss This 3662227 📰 Trump China Tariffs Rare Earths 9514888 📰 Watch Your Age Magically Shifttry The Hottest Datemyage App In 2024 8122061 📰 Game Tinju 2 Player 3715781 📰 Best Study Apps 8768606