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College Algebra Final Exam Review Assignment # 3 1. Use the properties of logarithms to find the exact value of the expression: log 8 64 + log 4 192 − log 4 3 − log 9 9 2. Solve the following inequality: 4𝑥 + 10 ≥6 𝑥+4 3. Use the polynomial function 𝑓(𝑥) = 𝑥 2 (𝑥 − 2)(𝑥 + 2) to answer the following questions: a. Find the degree of the polynomial and determine the end behavior. b. Find the x and y intercepts for the graph. For each x-intercept, determine whether the graph touches or crosses the x axis. c. Graph the polynomial with 2 additional points. 4. Write as the sum and/or difference of logarithms. Combine any like terms. 𝑥 2 + 2𝑥 log ( 2 ) (𝑥 − 𝑥 − 6)3 5. Solve algebraically. 1 1 2 − [log 4 𝑥 + log 4 (𝑥 − 6)] = − log 6 6 3 3 3 6. Find all the zeros of the polynomial function 𝑓(𝑥) = 𝑥 3 − 8𝑥 2 + 25𝑥 − 26 7. The half life of Magnesium-27 is 9.45 minutes. If a sample contains 30 grams of Magnesium-27, how much will be present after 20 minutes. 8. Graph the rational function: 2𝑥 2 − 5𝑥 + 2 𝑓(𝑥) = 𝑥2 − 4