8.5 properties of logarithms p. 493. properties of logarithms let b, u, and v be positive numbers...
TRANSCRIPT
![Page 1: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/1.jpg)
8.5Properties of logarithms
p. 493
![Page 2: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/2.jpg)
Properties of Logarithms• Let b, u, and v be positive numbers such
that b≠1.
• Product property:
• logbuv = logbu + logbv• Quotient property:
• logbu/v = logbu – logbv• Power property:
• logbun = n logbu
![Page 3: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/3.jpg)
Use log53≈.683 and log57≈1.209
• Approximate:
• log53/7 =
• log53 – log57 ≈
• .683 – 1.209 =
• -.526
•log521 =•log5(3·7)=•log53 + log57≈•.683 + 1.209 =•1.892
![Page 4: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/4.jpg)
Use log53≈.683 and log57≈1.209
• Approximate:
• log549 =
• log572 =
• 2 log57 ≈
• 2(1.209)=
• 2.418
![Page 5: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/5.jpg)
Expanding Logarithms
• You can use the properties to expand logarithms.
• log2 =
• log27x3 - log2y =
• log27 + log2x3 – log2y =
• log27 + 3·log2x – log2y
y
x37
![Page 6: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/6.jpg)
Your turn!• Expand:
• log 5mn =• log 5 + log m + log n
• Expand:
• log58x3 =• log58 + 3·log5x
![Page 7: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/7.jpg)
Condensing Logarithms
• log 6 + 2 log2 – log 3 =
• log 6 + log 22 – log 3 =
• log (6·22) – log 3 =
• log =
• log 8
3
26 2
![Page 8: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/8.jpg)
Your turn again!
• Condense:
• log57 + 3·log5t =• log57t3
• Condense:
• 3log2x – (log24 + log2y)=
• log2 y
x
4
3
![Page 9: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/9.jpg)
Change of base formula:
• u, b, and c are positive numbers with b≠1 and c≠1. Then:
• logcu =
• logcu = (base 10)
• logcu = (base e)
c
u
b
b
log
log
c
u
log
log
c
u
ln
ln
![Page 10: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/10.jpg)
Examples:
• Use the change of base to evaluate:
• log37 =• (base 10)
• log 7 ≈
• log 3
• 1.771
•(base e)•ln 7 ≈ •ln 3•1.771
![Page 11: 8.5 Properties of logarithms p. 493. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u](https://reader036.vdocuments.net/reader036/viewer/2022072011/56649de85503460f94ae211f/html5/thumbnails/11.jpg)
Assignmentpg. 496pg. 496
15 – 72 x 3’s and15 – 72 x 3’s and80-85 all80-85 all