Loading in 5 sec....

7-5 Properties of LogarithmsPowerPoint Presentation

7-5 Properties of Logarithms

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

7-5 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 - - - - - - - - - - - - - - - - - - - - - - - - - -

7-5 Properties of Logarithms

Rolling them out and Wrapping them up

- 1. Product Property
- 2. QuotientProperty
- 3. Power Property
- The above will be on the quiz!

- b, m, & n must be positive numbers and b ≠ 1
- log bmn = log b m + log b n
- Examples:
- log 4 21 = log 4 (3 · 7)
= log 4 3 + log 4 7

- log 3 27 = log 3 (3 * 9)
= log 3 3 + log 3 9

= 1 + 2

= 3

- log 3 4x = log 3 4 + log 3 x

- log 4 21 = log 4 (3 · 7)

- b, m, & n must be positive numbers and b ≠ 1
- log b = log b m – log b n
- Examples:
- log 4 = log 4 3 – log 4 7
- log 3 = log 3 2 – log 3 x

- Notice the numerator is listed first and the denominator is subtracted from it

m

n

3

7

2

x

- b, m, & n must be positive numbers and b ≠ 1
- log bmn = n log b m
- Examples:
- log 4 49 = log 4 72
= 2 log 4 7

- log 2 512 = log 2 83
= 3 log 2 8

= 3 · 3

= 9

- log 4 49 = log 4 72

- log 6 =log 6 5x3 – log 6 y Quotient Property
= log 6 5 + log 6 x3 – log 6 y Product Property

= log 6 5 + 3 log 6 x – log 6 y Power Property

5x3

y

Using properties to condense an expression

- 5 log 4 2 + 7 log 4 x – 4 log 4 y
- log 4 25 + log 4 x7 – log 4 y4Power Property
- log 4 25x7 – log 4 y4 Product Property
- log4 = log 4Quotient Property & Simplify

32x7

y4

25x7

y4

- log 3 8 = ≈
- ≈ 1.893

log 8

log 3

0.9031

0.4771