4.3 Laws of ExponentsRomans 8:24-25 For in this hope we were saved.Now hope that is seen is not hope. For who hopes forwha...
Remember that logs are exponents.Therefore, these laws should make sense ...
Remember that logs are exponents.Therefore, these laws should make sense ...1)   log a (AB) = log a A + log a B
Remember that logs are exponents.Therefore, these laws should make sense ...1)   log a (AB) = log a A + log a B         ⎛...
Remember that logs are exponents.Therefore, these laws should make sense ...1)   log a (AB) = log a A + log a B         ⎛...
Logs can be manipulated using these lawsto either expanded form or combined form.
Expand1) log 3 (9x)
Expand1) log 3 (9x)    log 3 9 + log 3 x
Expand1) log 3 (9x)    log 3 9 + log 3 x    2 + log 3 x
Expand2) log 7 (x y )           3 4
Expand2) log 7 (x y )           3 4          3             4    log 7 x + log 7 y
Expand2) log 7 (x y )           3 4           3            4    log 7 x + log 7 y    3log 7 x + 4 log 7 y
Expand      ⎛ a b ⎞3) ln ⎜ 8 ⎟      ⎝ c ⎠
Expand      ⎛ a b ⎞3) ln ⎜ 8 ⎟      ⎝ c ⎠             1        ⎛    ⎞     ln ⎜ ab ⎟ − ln ( c )             2    ...
Expand      ⎛ a b ⎞3) ln ⎜ 8 ⎟      ⎝ c ⎠             1        ⎛    ⎞     ln ⎜ ab ⎟ − ln ( c )             2    ...
Expand      ⎛ a b ⎞3) ln ⎜ 8 ⎟      ⎝ c ⎠             1        ⎛    ⎞     ln ⎜ ab ⎟ − ln ( c )             2    ...
Combine          34) 3ln x + ln ( x + 3)          2
Combine          34) 3ln x + ln ( x + 3)          2                         3        3    ln x + ln ( x + 3)   2
Combine          34) 3ln x + ln ( x + 3)          2                          3        3    ln x + ln ( x + 3)    2        ...
Combine            3  4) 3ln x + ln ( x + 3)            2                            3          3      ln x + ln ( x + 3) ...
Combine5)   log x − 3log y + log ( x + y )
Combine  5)   log x − 3log y + log ( x + y )order of operations ... from left to right
Combine  5)   log x − 3log y + log ( x + y )order of operations ... from left to right           ⎛ x          ⎞       lo...
Combine     3                     16)     ln (16y ) − 2 ln x + ln y     4                     4
Combine     3                     16)     ln (16y ) − 2 ln x + ln y     4                     4             3             ...
Combine     3                     16)     ln (16y ) − 2 ln x + ln y     4                     4             3             ...
Combine     3                     16)     ln (16y ) − 2 ln x + ln y     4                     4             3             ...
Combine     3                     16)     ln (16y ) − 2 ln x + ln y     4                     4             3             ...
Remember: Change of Base Formula
Remember: Change of Base Formula                 log x ln x       log b x =      =                 logb lnb
True or False? (Group Consensus)        calculator ok to use ...
True or False? (Group Consensus)                calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5      7 log ...
True or False? (Group Consensus)                calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5     False  ...
True or False? (Group Consensus)                calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5     False  ...
True or False? (Group Consensus)                calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5     False  ...
True or False? (Group Consensus)                calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5     False  ...
HW #6I’ve got a theory that if you give 100% all of the time,somehow things will work out in the end.                     ...
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0406 ch 4 day 6

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  • 0406 ch 4 day 6

    1. 1. 4.3 Laws of ExponentsRomans 8:24-25 For in this hope we were saved.Now hope that is seen is not hope. For who hopes forwhat he sees? But if we hope for what we do notsee, we wait for it with patience.
    2. 2. Remember that logs are exponents.Therefore, these laws should make sense ...
    3. 3. Remember that logs are exponents.Therefore, these laws should make sense ...1) log a (AB) = log a A + log a B
    4. 4. Remember that logs are exponents.Therefore, these laws should make sense ...1) log a (AB) = log a A + log a B ⎛ A ⎞2) log a ⎜ ⎟ = log a A − log a B ⎝ B ⎠
    5. 5. Remember that logs are exponents.Therefore, these laws should make sense ...1) log a (AB) = log a A + log a B ⎛ A ⎞2) log a ⎜ ⎟ = log a A − log a B ⎝ B ⎠3) c log a (A) = c log a A
    6. 6. Logs can be manipulated using these lawsto either expanded form or combined form.
    7. 7. Expand1) log 3 (9x)
    8. 8. Expand1) log 3 (9x) log 3 9 + log 3 x
    9. 9. Expand1) log 3 (9x) log 3 9 + log 3 x 2 + log 3 x
    10. 10. Expand2) log 7 (x y ) 3 4
    11. 11. Expand2) log 7 (x y ) 3 4 3 4 log 7 x + log 7 y
    12. 12. Expand2) log 7 (x y ) 3 4 3 4 log 7 x + log 7 y 3log 7 x + 4 log 7 y
    13. 13. Expand ⎛ a b ⎞3) ln ⎜ 8 ⎟ ⎝ c ⎠
    14. 14. Expand ⎛ a b ⎞3) ln ⎜ 8 ⎟ ⎝ c ⎠ 1 ⎛ ⎞ ln ⎜ ab ⎟ − ln ( c ) 2 8 ⎝ ⎠
    15. 15. Expand ⎛ a b ⎞3) ln ⎜ 8 ⎟ ⎝ c ⎠ 1 ⎛ ⎞ ln ⎜ ab ⎟ − ln ( c ) 2 8 ⎝ ⎠ 1 8 ln a + lnb − ln c 2
    16. 16. Expand ⎛ a b ⎞3) ln ⎜ 8 ⎟ ⎝ c ⎠ 1 ⎛ ⎞ ln ⎜ ab ⎟ − ln ( c ) 2 8 ⎝ ⎠ 1 8 ln a + lnb − ln c 2 1 ln a + lnb − 8 ln c 2
    17. 17. Combine 34) 3ln x + ln ( x + 3) 2
    18. 18. Combine 34) 3ln x + ln ( x + 3) 2 3 3 ln x + ln ( x + 3) 2
    19. 19. Combine 34) 3ln x + ln ( x + 3) 2 3 3 ln x + ln ( x + 3) 2 3 ⎛ 3 ⎞ ln ⎜ x ( x + 3) ⎟ 2 ⎝ ⎠
    20. 20. Combine 3 4) 3ln x + ln ( x + 3) 2 3 3 ln x + ln ( x + 3) 2 3 ⎛ 3 ⎞ ln ⎜ x ( x + 3) ⎟ 2 ⎝ ⎠Book answer could be: ( ln x 3 ( x + 3) 3 )
    21. 21. Combine5) log x − 3log y + log ( x + y )
    22. 22. Combine 5) log x − 3log y + log ( x + y )order of operations ... from left to right
    23. 23. Combine 5) log x − 3log y + log ( x + y )order of operations ... from left to right ⎛ x ⎞ log ⎜ 3 ( x + y )⎟ ⎝ y ⎠
    24. 24. Combine 3 16) ln (16y ) − 2 ln x + ln y 4 4
    25. 25. Combine 3 16) ln (16y ) − 2 ln x + ln y 4 4 3 1 2 ln (16y ) − ln x + ln y 4 4
    26. 26. Combine 3 16) ln (16y ) − 2 ln x + ln y 4 4 3 1 2 ln (16y ) − ln x + ln y 4 4 3 1 ⎛ ⎞ 2 ln ⎜ 8y ⎟ + ln y − ln x 4 4 ⎝ ⎠
    27. 27. Combine 3 16) ln (16y ) − 2 ln x + ln y 4 4 3 1 2 ln (16y ) − ln x + ln y 4 4 3 1 ⎛ ⎞ 2 ln ⎜ 8y ⎟ + ln y − ln x 4 4 ⎝ ⎠ 3 1 ⎛ ⎞ 2 ln ⎜ 8y y ⎟ − ln x 4 4 ⎝ ⎠
    28. 28. Combine 3 16) ln (16y ) − 2 ln x + ln y 4 4 3 1 2 ln (16y ) − ln x + ln y 4 4 3 1 ⎛ ⎞ 2 ln ⎜ 8y ⎟ + ln y − ln x 4 4 ⎝ ⎠ 3 1 ⎛ ⎞ 2 ln ⎜ 8y y ⎟ − ln x 4 4 ⎝ ⎠ 8y ln 2 x
    29. 29. Remember: Change of Base Formula
    30. 30. Remember: Change of Base Formula log x ln x log b x = = logb lnb
    31. 31. True or False? (Group Consensus) calculator ok to use ...
    32. 32. True or False? (Group Consensus) calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5 7 log 72) log = 2 log 23) 4 ln 6 = ln 6 4 44) 4 ln 6 = ( ln 6 )
    33. 33. True or False? (Group Consensus) calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5 False 7 log 72) log = 2 log 23) 4 ln 6 = ln 6 4 44) 4 ln 6 = ( ln 6 )
    34. 34. True or False? (Group Consensus) calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5 False 7 log 72) log = False 2 log 23) 4 ln 6 = ln 6 4 44) 4 ln 6 = ( ln 6 )
    35. 35. True or False? (Group Consensus) calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5 False 7 log 72) log = False 2 log 23) 4 ln 6 = ln 6 4 True 44) 4 ln 6 = ( ln 6 )
    36. 36. True or False? (Group Consensus) calculator ok to use ...1) log10 ( 3 + 5 ) = log10 3 + log10 5 False 7 log 72) log = False 2 log 23) 4 ln 6 = ln 6 4 True 44) 4 ln 6 = ( ln 6 ) False
    37. 37. HW #6I’ve got a theory that if you give 100% all of the time,somehow things will work out in the end. Larry Bird

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