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Section 6.4. Properties of Logarithmic Functions Objectives: Simplify and evaluate expressions involving logarithms. Solve equations involving logarithms. Standard: 2.8.11.N. Solve equations. Product and Quotient Properties of Exponents

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Presentation Transcript
slide2

Section 6.4

    • Properties of Logarithmic Functions
  • Objectives:
  • Simplify and evaluate expressions involving logarithms.
  • Solve equations involving logarithms.
  • Standard:
  • 2.8.11.N. Solve equations.
slide3

Product and Quotient Properties of Exponents

am • an = am+n Product Property

am/an = am-n Quotient Property

(am)n = am*n Power Property

slide4

Product and Quotient Properties of Logarithms

For m > 0, n > 0, b > 0, and b ≠ 1:

Product Property

logb (mn) = logbm + logbn

Quotient Property

logb (m/n) = logbm – logbn

** Just like the exponent rules!

slide5

A.

log2 12

= log2 (2 ● 2 ● 3)

= log2 2 + log2 2 + log2 3

≈1 + 1 + 1.5850

≈3.5850

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B.

log2 1.5

= log2 3/2

= log2 3 – log2 2

≈1.5850 - 1

≈0.5850

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C. log 2 18

D. log2 .75

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Write each expression as a single logarithm. Then simplify, if possible.

A. log3 10 – log3 5

B. logb u + logb v – logb uw

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C. log4 18 – log4 6

D. logb 4x - logb 3y + logb y

slide10

Power Property of Logarithms

For m > 0, b > 0, b ≠ 1, and any real number p:

logb mp = p logb m

Ex 3.

Evaluate log5 254

Log5 254 = 4 log5 25

= 4 ● 2

= 8

power property of logarithms
Power Property of Logarithms

Ex 4.

Evaluate log3 27100

slide12

Exponential- Logarithmic Inverse Properties:

For b > 0, b ≠1:

logb bx = x and blogbx = x for x > 0.

A. 3log34 + log5 25

B. log2 32 – 5log53

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C.

7log711 + log381

D.

log885 +3log38

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Homework

Integrated Algebra II- Section 6.4 Level A

Honors Algebra II- Section 6.4 Level B

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