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Basic Logarithms

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Basic Logarithms

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  1. Basic Logarithms A way to Undo exponents

  2. Many things we do in mathematics involve undoingan operation.

  3. Subtraction is the inverse of addition

  4. When you were in grade school, you probably learned about subtraction this way. 2 + = 8 7 + = 10

  5. Then one day your teacher introduced you to a new symbol ─ to undo addition

  6. 3 + = 10 Could be written 10 ─ 3 =

  7. 8 – 2 =

  8. 8 – 2 = 2 + ? = 8

  9. 8 – 2 = 2 + 6 = 8

  10. 8 – 2 = 6 2 + 6 = 8

  11. The same could be said about division÷

  12. 40 ÷ 5 =

  13. 40 ÷ 5 = 5 x ? = 40

  14. 40 ÷ 5 = 5 x 8 = 40

  15. 40 ÷ 5 = 8 5 x 8 = 40

  16. Consider √49

  17. = ?

  18. = ? ?2 = 49

  19. = ? 72 = 49

  20. = 7 72 = 49

  21. Exponential Equations: 5? = 25

  22. Exponential Equations: 52 = 25

  23. Logarithmic Form of 52= 25 islog525 = 2

  24. log525 =?

  25. log525 =? 5? = 25

  26. log525 =? 52 = 25

  27. log525 =2 52 = 25

  28. Try this one…

  29. log749 =?

  30. log749 =? 7? = 49

  31. log749 =? 72 = 49

  32. log749 =2 72 = 49

  33. and this one…

  34. log327 =?

  35. log327 =? 3? = 27

  36. log327 =? 33 = 27

  37. log327 =3 33 = 27

  38. Remember your exponent rules? 70 = ? 50 = ?

  39. Remember your exponent rules? 70 = 1 50 = 1

  40. log71 =?

  41. log71 =? 7? = 1

  42. log71 =? 70 = 1

  43. log71 =0 70 = 1

  44. Keep going…

  45. log31 =?

  46. log31 =? 3? = 1

  47. log31 =? 30 = 1

  48. log31 =0 30 = 1

  49. Remember this? 1/25 = 1/ 52=5-2

  50. log5()=?