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Certainly! The text from the image outlines some mathematical problems involving inequalities and logarithmic functions. Here’s a brief breakdown of what each section asks you to do: 7.7 Find the solution sets for the following inequalities: 1. \( \log_3 (x^2 - 1) \leq \log_3 (2x + 3) \) 2. \( \log_3 (x + 2) \geq \log_3 (x - 1) \) 3. \( \log_5 (2x - 3) > \log_5 (x + 4) \) 4. Solve: \( \log_6 (x + 1) + \log_6 (x - 1) = \log_6 (10x + 11) \) 5. \( \log_3 (x^2 + x + 31) \leq \log_3 (10x + 11) \) 7.8 Solve inequalities: 1. \( \log_2 (2x - 3) < \log_2 (x + 1) \) 2. \( \log_2 \left(\frac{x+2}{4}\right) \leq \log_2 (x - 1) \) 3. \( \log_5 (3x) > \log_5 (2x + 1) \) Keep in mind that when solving these problems, properties of logarithms are used, including rules for when inequalities flip signs. If two logarithms with the same base are being compared, you can compare the numbers inside the logs directly, provided those numbers are within the domain of the logs.