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# 7-5 Properties of Logarithms PowerPoint PPT Presentation

7-5 Properties of Logarithms. Rolling them out and Wrapping them up. Definitions. 1. Product Property 2 . Quotient Property 3 . Power Property The above will be on the quiz!. Product Property. b, m, & n must be positive numbers and b ≠ 1 l og b mn = log b m + log b n

7-5 Properties of Logarithms

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## 7-5 Properties of Logarithms

Rolling them out and Wrapping them up

### Definitions

• 1. Product Property

• 2. QuotientProperty

• 3. Power Property

• The above will be on the quiz!

### Product Property

• 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

### Quotient Rule

• 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

### Power Property

• 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

### Using properties to expand an expression

• 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