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37. −2e 21. e −5x + 19 = 3 ANSWER: 0.6931 7-7 Base e and Natural Logarithms Write an equivalent exponential or logarithmic function. 3x 39. −4e −x +9=2 ANSWER: −0.5596 = 0.1 ANSWER: ln 0.1 = −5x Solve each inequality. Round to the nearest tenthousandth. x 23. ln 5.4 = x 41. e ≤ 8.7 ANSWER: {x | x ≤ 2.1633} ANSWER: x 5.4 = e 25. ln (x + 4) = 36 3 43. ln (3x + 4) > 10 ANSWER: e 36 ANSWER: {x | x > 8.0105} =x+4 x 27. ln e = 7 4 45. ln (8x ) > 24 ANSWER: 7 ANSWER: x e =e Write each as a single logarithm. 29. 3 ln 10 + 2 ln 100 ANSWER: 7 ln 10 31. ANSWER: −2 ln 2 2 33. 3 ln x + 4 ln 3 47. FINANCIAL LITERACY Use the formula for continuously compounded interest. a. If you deposited $800 in an account paying 4.5% interest compounded continuously, how much money would be in the account in 5 years? b. How long would it take you to double your money? c. If you want to double your money in 9 years, what rate would you need? d. If you want to open an account that pays 4.75% interest compounded continuously and have $10,000 in the account 12 years after your deposit, how much would you need to deposit? ANSWER: ln 81x ANSWER: a. $1001.86 b. about 15.4 yr c. about 7.7% d. about $5655.25 6 Solve each equation. Round to the nearest tenthousandth. x 35. 4e + 2 = 180 Write the expression as a sum or difference of logarithms or multiples of logarithms. ANSWER: 3.7955 49. 37. −2e 3x + 19 = 3 ANSWER: 0.6931 ANSWER: 4 ln 2 − 3 ln 5 4 −3 −x + 9 =- Powered 2 39. −4e Manual eSolutions by Cognero ANSWER: −0.5596 51. ln xy z ANSWER: ln x + 4 ln y − 3 ln z Page 1 49. ANSWER: 7-7 Base andlnNatural Logarithms 4 ln 2e− 3 5 4 −3 51. ln xy z ANSWER: ln x + 4 ln y − 3 ln z Use the natural logarithm to solve each equation. x 53. 3 = 0.4 ANSWER: about −0.8340 2x 55. 5 = 38 ANSWER: about 1.1301 eSolutions Manual - Powered by Cognero Page 2