For the following exercises, use logarithms to solve 11.911 14. 2 10M29 17. e* +

Question

For the following exercises, use logarithms to solve 11.911 14. 2 10M29 17. e* +6-44 20. 252*' 23. 10e++2 8 26. 3 7*-2 For the following exercises, use the definition of a logarithm to rewrite the equation as an exponential equation 29. log 100 For the following exercises, use the definition of a logarithm to solve the equation 31. 5log,(n) 10 13. e10-10--42 16, 7e3"-5 + 5=-89 19. -6e9*+2-74 12. 2e 13 15.-8 10+7-7-24 24. 4e*+3-7 53 x-24-90 28. 3e631 30, 108,24(18) 32. -8log,(x)-16 35. 10 4ln(9 8x) 6 log(8m + 4) + 6 = 10 For the following exercises, use the one-to-one property of logarithms to solve 36. In(10-3x) In(-4x) 39. In(-3x)Inx-6x) 42. log,(2??14m)s log(-45 + ?) 43. In(x2-10) + In(9) In( 10) 37. log, ,(5n-2) log (8-5) 38. logx+3) log(x) log(74) 40. log,(6 -m)-log,3(m) 41. In(x- 2) In(x) In(54) For the following exercises, solve each equation for x 44. log(x +12)-log(x) + log(12) 45. In(x)In(x 47. In(7)In(2-4x) In(14) 50, log,(3x)-log,(6) = log,(77) 3 In(7x) 40, log,(7x + 6) = 3 ogx 6)-log,(x)-log,(58) 49. In(3) In(3-3x)-In(4)

Explanation / Answer

21) e^2x - e^x - 132 = 0

let e^x = y

so, equation in terms of y is

y^2 - y - 132 = 0

y = -11 , 12

e^x = -11

e^x = 12

x = ln 12

x = 2.485

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