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Solve and give exact values. Simplify 1) log 5x = log (2x + 9) 2) log (10 − 4x) = log (10 − 3x) 3) log (4p − 2) = log (−5p + 5) 4) log 2 3x − log 2 7 = 3 5) −10 + log 3 (n + 3) = −10 7) log 3 8+ log 3 6) −2log 5 7x = 2 −5x = 3 8) log 6 5 − log 6 (x − 7) = 1 9. 7𝑥+4 = 49𝑥+3 10. 324𝑥+3 = 42𝑥−5 12. 10𝑥−5 = 0.1𝑥−4 1 10+𝑥 11. 644𝑥−2 = (8) Expand/Contract. Be Sure to simplify !!! 2𝑥 10𝑥 2 𝑤 3 𝑧 7 13. ln (𝑒 𝑥 ) 14. log 15. 5 log 5 𝑥 − log 5 (𝑥 − 5) 16. 3 ln 𝑥 4 − 3 ln 𝑥 + ln 8 17. log(𝑥 − 3) + log(𝑥 + 1) − log(𝑥 2 − 2𝑥 − 3) + log 7 18. −5log(3𝑥) − log 𝑤 + log 3𝑥 2𝑥 3 𝑦 1 19. Graph the following, showing all critical points and asymptotes. (4 points each) 𝑦 = 𝑒 −𝑥 𝑦 = − log 3 (𝑥 + 3) − 2 1 𝑥+1 𝑓(𝑥) = (4) +1 𝑓(𝑥) = ln(−𝑥 + 2) + 2 Solve the logarithmic equation. Round answers to the thousandth. 20. 8 t 6 21. 4 15 e x 8 22. 1 log( x 3) 23. log( x 3) 24. 1 log 4 2 log 4 (3 x) 25. log( t 3) log( t ) 1 26. log 2 (t 1) log 2 (t 1) 5 27. 2 log( 2) log( 3 x) 28. ln( 4t ) ln( 3t ) 2 29. log 2 (t 1) log 2 (t 1) 3 1 2 Solve each problem by using the appropriate formula. Interest formulas are located below. 𝑟 𝑛𝑡 𝐴 = 𝑃 ∙ (1 + 𝑛) 𝐴 = 𝑃𝑒 𝑟𝑡 30. Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4.25% interest compounded semi-annually. How much will be in Kelly’s account at the end of four years? 31. If you invested $1,000 in an account paying an annual percentage rate (quoted rate) of 12%, compounded weekly, how much would you have in your account at the end of 1 year, 10 years, 20 years, 100 years? 32. ABC Bank is offering to double your money! They say that if you invest with them at 6% interest compounded quarterly they will double your money. If you invest $1500 in the account, how long will it take to double your money 33. If interest is compounded continuously at 4.5% for 7 years, how much will a $2000 investment be worth at the end of 7 years? 34. How long will it take $3000 to double if it is invested in an account that pays 3% compounded continuously? 35. Since January 1980, the population of the city of Brownville has grown according to the mathematical model y 720,500(1.022) x , where x is the number of years since January 1980. a) Explain what the numbers 720,500 and 1.022 represent in this model. b) What would the population be in 2000 if the growth continues at the same rate. c) Use this model to predict about when the population of Brownville will first reach 1,000,000. 36. The half-life of a medication is the amount of time for half of the drug to be eliminated from the body. The half-life of Advil or ibuprofen is represented by the equation R M (0.5) t 2 , where R is the amount of Advil remaining in the body, M is the initial dosage, and t is time in hours. a) A 200 milligram dosage of Advil is taken at 1:00 pm. How many milligrams of the medication will remain in the body at 6:00 pm? b) If a 200 milligram dosage of Advil is taken, how many milligrams of the medication will remain in the body 12 hours later?