Loading in 5 sec....

8.5 Properties of logarithmsPowerPoint Presentation

8.5 Properties of logarithms

- 75 Views
- Uploaded on
- Presentation posted in: General

8.5 Properties of logarithms

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

8.5Properties of logarithms

p. 493

- 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

- Approximate:
- log53/7 =
- log53 – log57 ≈
- .683 – 1.209 =
- -.526

- log521 =
- log5(3·7)=
- log53 + log57≈
- .683 + 1.209 =
- 1.892

- Approximate:
- log549 =
- log572 =
- 2 log57 ≈
- 2(1.209)=
- 2.418

- You can use the properties to expand logarithms.
- log2 =
- log27x3 - log2y =
- log27 + log2x3 – log2y =
- log27 + 3·log2x – log2y

- Expand:
- log 5mn=
- log 5 + logm + logn
- Expand:
- log58x3 =
- log58 + 3·log5x

- log 6 + 2 log2 – log 3 =
- log 6 + log 22 – log 3 =
- log (6·22) – log 3 =
- log =
- log 8

- Condense:
- log57 + 3·log5t =
- log57t3
- Condense:
- 3log2x – (log24 + log2y)=
- log2

- u, b, and c are positive numbers with b≠1 and c≠1. Then:
- logcu =
- logcu = (base 10)
- logcu = (base e)

- Use the change of base to evaluate:
- log37 =
- (base 10)
- log 7 ≈
- log 3
- 1.771

- (base e)
- ln 7≈
- ln 3
- 1.771