Solutions
Solutions to Try Its
1. a. is equivalent to b. is equivalent to 2. a. is equivalent to b. is equivalent to c. is equivalent to 3. (recalling that ) 4. 5. It is not possible to take the logarithm of a negative number in the set of real numbers. 6. It is not possible to take the logarithm of a negative number in the set of real numbers.Solutions to Odd-Numbered Exercises
1. A logarithm is an exponent. Specifically, it is the exponent to which a base b is raised to produce a given value. In the expressions given, the base b has the same value. The exponent, y, in the expression can also be written as the logarithm, , and the value of x is the result of raising b to the power of y. 3. Since the equation of a logarithm is equivalent to an exponential equation, the logarithm can be converted to the exponential equation , and then properties of exponents can be applied to solve for x. 5. The natural logarithm is a special case of the logarithm with base b in that the natural log always has base e. Rather than notating the natural logarithm as , the notation used is . 7. 9. 11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37. 32 39. 1.06 41. 14.125 43. 45. 4 47. –3 49. –12 51. 0 53. 10 55. 2.708 57. 0.151 59. No, the function has no defined value for x = 0. To verify, suppose x = 0 is in the domain of the function . Then there is some number n such that . Rewriting as an exponential equation gives: , which is impossible since no such real number n exists. Therefore, x = 0 is not the domain of the function . 61. Yes. Suppose there exists a real number x such that . Rewriting as an exponential equation gives , which is a real number. To verify, let . Then, by definition, . 63. No; , so is undefined. 65. 2Licenses & Attributions
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- Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175..