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8.5 – Using Properties of Logarithms

8.5 – Using Properties of Logarithms. Product Property:. Product Property: log b mn. Product Property: log b mn = log b m. Product Property: log b mn = log b m + log b n. Product Property: log b mn = log b m + log b n Ex. Product Property: log b mn = log b m + log b n Ex. log 9 5 x.

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8.5 – Using Properties of Logarithms

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  1. 8.5 – Using Properties of Logarithms

  2. Product Property:

  3. Product Property:logbmn

  4. Product Property:logbmn = logbm

  5. Product Property:logbmn = logbm + logbn

  6. Product Property:logbmn = logbm + logbn Ex.

  7. Product Property:logbmn = logbm + logbn Ex.log95x

  8. Product Property:logbmn = logbm + logbn Ex.log95x = log95

  9. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x

  10. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property:

  11. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m n

  12. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm n

  13. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n

  14. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex.

  15. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x 9

  16. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x 9

  17. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x– log99 9

  18. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x– log99 9 • Power Property:

  19. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x– log99 9 • Power Property: logb mp

  20. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x– log99 9 • Power Property: logb mp = plogbm

  21. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x– log99 9 • Power Property: logb mp = plogbm

  22. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x– log99 9 • Power Property: logb mp = plogbm Ex.

  23. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x– log99 9 • Power Property: logb mp = plogbm Ex. log9x7

  24. Product Property:logbmn = logbm + logbn Ex.log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9x = log9x– log99 9 • Power Property: logb mp = plogbm Ex. log9x7 = 7log9x

  25. Ex. 2 Solve the following equations. a. 3 log5 x– log5 4 = log5 16

  26. Ex. 2 Solve the following equations. a. 3log5 x– log5 4 = log5 16 log5 x3– log5 4 = log5 16

  27. Ex. 2 Solve the following equations. a. 3 log5 x– log5 4 = log5 16 log5 x3–log54 = log5 16 log5 x3 = log5 16 4

  28. Ex. 2 Solve the following equations. a. 3 log5 x– log5 4 = log5 16 log5 x3– log5 4 = log5 16 log5x3 = log5 16 4

  29. Ex. 2 Solve the following equations. a. 3 log5 x– log5 4 = log5 16 log5 x3– log5 4 = log5 16 log5 x3 = log5 16 4 x3 = 16 4

  30. Ex. 2 Solve the following equations. a. 3 log5 x– log5 4 = log5 16 log5 x3– log5 4 = log5 16 log5 x3 = log5 16 4 x3 = 16 4 x3 = 64

  31. Ex. 2 Solve the following equations. a. 3 log5 x– log5 4 = log5 16 log5 x3– log5 4 = log5 16 log5 x3 = log5 16 4 x3 = 16 4 x3 = 64 x = 4

  32. b. log4 x– log4 (x – 6) = 2

  33. b. log4 x–log4(x – 6) = 2 log4 x= 2 x – 6

  34. b. log4 x– log4 (x – 6) = 2 log4 x= 2 x – 6 Change to exponential form!!!

  35. b. log4 x– log4 (x – 6) = 2 log4x=2 x – 6 42=x x – 6

  36. b. log4 x– log4 (x – 6) = 2 log4 x= 2 x – 6 42=x x – 6 16 =x x – 6

  37. b. log4 x– log4 (x – 6) = 2 log4 x= 2 x – 6 42=x x – 6 16=x 1 x – 6

  38. b. log4 x– log4 (x – 6) = 2 log4 x= 2 x – 6 42=x x – 6 16 =x x – 6 16(x – 6) = x

  39. b. log4 x– log4 (x – 6) = 2 log4 x= 2 x – 6 42=x x – 6 16 =x x – 6 16(x – 6) = x 16x – 96 = x

  40. b. log4 x– log4 (x – 6) = 2 log4 x= 2 x – 6 42=x x – 6 16 =x x – 6 16(x – 6) = x 16x – 96 = x 15x = 96

  41. b. log4 x– log4 (x – 6) = 2 log4 x= 2 x – 6 42=x x – 6 16 =x x – 6 16(x – 6) = x 16x – 96 = x 15x = 96 x = 96/15

  42. b. log4 x– log4 (x – 6) = 2 log4 x= 2 x – 6 42=x x – 6 16 =x x – 6 16(x – 6) = x 16x – 96 = x 15x = 96 x = 96/15 x = 32/5

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