Properties of logarithmic functions objectives
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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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Properties of logarithmic functions objectives

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.


  • Properties of logarithmic functions objectives

    Product and Quotient Properties of Exponents

    am • an = am+n Product Property

    am/an = am-n Quotient Property

    (am)n = am*n Power Property


    Properties of logarithmic functions objectives

    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!


    Properties of logarithmic functions objectives

    A.

    log2 12

    = log2 (2 ● 2 ● 3)

    = log2 2 + log2 2 + log2 3

    ≈1 + 1 + 1.5850

    ≈3.5850


    Properties of logarithmic functions objectives

    B.

    log2 1.5

    = log2 3/2

    = log2 3 – log2 2

    ≈1.5850 - 1

    ≈0.5850


    Properties of logarithmic functions objectives

    C. log 2 18

    D. log2 .75


    Properties of logarithmic functions objectives

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

    A. log3 10 – log3 5

    B. logb u + logb v – logb uw


    Properties of logarithmic functions objectives

    C. log4 18 – log4 6

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


    Properties of logarithmic functions objectives

    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


    Properties of logarithmic functions objectives

    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


    Properties of logarithmic functions objectives

    C.

    7log711 + log381

    D.

    log885 +3log38


    Properties of logarithmic functions objectives

    Homework

    Integrated Algebra II- Section 6.4 Level A

    Honors Algebra II- Section 6.4 Level B


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