University:
Montgomery College
Course:
MATH 050: Foundations of Algebra
Academic year:

2019
Views:

275

Pages:

2
Author:

Tobsuchtbvow

Logarithm Basics: For every logarithmic equation of the form N X exponential equation: log b X log b X there is an exactly equivalent bN is “the logarithm to the base b of X” and is the number to which you raise b in order to get X So we can think of logarithms as powers of the base, b . “Taking the logarithm of” and “raising to a power” are inverse operations, i.e., each “undoes” the other: log b bN N and X b logb X For every rule for exponents there is a corresponding rule for logarithms: Exponents Logarithms b 1 log b 1 0 b b log b b 1 1⁄b b bN ∗ bM bN / bM bN M bN M bN M ln X 1 log b X ∗ Y log b X log b X/Y log b X N bN∗M By convention: log X log b 1⁄b log log e X where e ≅ 2.718 X log b X log b Y log b Y N ∗ log b X Rule for changing base (e. g., to base 10): log b X log(X) log(b) Logarithms of integers up to 10: N 2 log(N) 0.30 3 4 0.48 0.60 5 6 0.70 0.78 7 0.85 8 9 0.90 0.95 Exercises: For each of 1 – 8, match the expression or equation with an equivalent expression or equation in a) – h). 3. log 5 1. log 25 2. 2 5. log 5X 6. log X 27 a) 1 b) X g) 2 h) 0 c) X X 27 5 2X 7. 8 d) log X 4. log 1 e) log 8 5 5 8. X X f) log X 5 2 0.01 Simplify: 9. log 10. log 16 11. log 1 12. log 9 13. log 14. log 8 15. log 8 16. log 17. log 18. log 125 19. log 3 20. log 27 21. log 24. log 1000 ⁄ ⁄ 25. log 9 3 ∗ log 81 22. log 64 23. 6 26. log log log 81 Solve: 2 29. log 2X 1 1 2 12. 5 11. 0 2. d Answers: 1. g 13. – 2 14. 3 3. a 4. h 15. 3 5. b 26. 0 27. 1 9 , 9 28. 6 16. –1 17. –2 6. c 7. e 18. 3 8. f 21X X 2 25. 1 30. log 28. log 3X 24. 3 2 21. 2 3 22. 3 2 23. 13 27. | log X | 29. 7 16 30. 19. ⁄ 9. 3 20. ⁄ 10. 4 25, 4