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Transcript of UNIT 11 LESSON 3 PROPERTIES OF LOGARITHMS · PDF file UNIT 11 LESSON 3 PROPERTIES OF...

  • UNIT 11 LESSON 3

    PROPERTIES OF LOGARITHMS

    COLLEGE PREP

  • OBJECTIVES

    • Understand properties of logarithms

    • Expand and condense logarithms

    • Evaluate logarithms without common bases (10,𝑒)

  • Inverse Property

    INVERSE PROPERTY OF LOGARITHMS

    𝑎log𝑎 𝑀 = 𝑀 log𝑎 𝑎

    𝑟 = 𝑟

    Logs and exponentials are inverses. If their bases match, they cancel each other out.

  • Inverse Property

    Evaluate each logarithm.

    A) 3log3 17 B) 0.5log0.5 11

    C) log2 2 6 D) ln 𝑒7

  • Product Rule

    PRODUCT RULE OF LOGARITHMS

    log𝑎 𝑀𝑁 = log𝑎𝑀 + log𝑎 𝑁

  • Product Rule

    Write each expression as the sum of logs.

    E) log3(9𝑥) F) ln(2𝑘)

  • Quotient Rule

    QUOTIENT RULE OF LOGARITHMS

    log𝑎 𝑀

    𝑁 = log𝑎𝑀 − log𝑎 𝑁

  • Quotient Rule

    Write each expression as the difference of logs.

    G) log4 𝑥

    16 H) log

    𝑠

    𝑡

  • Expand Logarithms

    Expand the logarithm completely.

    I) log4 3𝑥

    𝑦 J) ln

    𝑎

    5𝑏𝑐

  • Power Rule

    POWER RULE OF LOGARITHMS

    log𝑎𝑀 𝑟 = 𝑟𝑙𝑜𝑔𝑎𝑀

  • Power Rule

    Expand the logarithm completely.

    K) log7 2 4 L) ln 𝑥

  • Expand Logarithms

    Expand the logarithm completely.

    M) log3(9𝑥 2𝑦4) N)log

    100𝑥

    𝑦

  • Condense Logarithms

    Condense the logarithm completely.

    O) log4 2 + log4 8 P) ln 𝑥 + 3 − ln 𝑥

  • Condense Logarithms

    Condense the logarithm completely.

    Q) 1

    2 log3 𝑥 + 2 + 2 log3 𝑥

  • Condense Logarithms

    Condense the logarithm completely.

    R) log2 9 + 2 log2 𝑥 − log2 𝑥 − 4

  • Change of Base Formula

    To calculate logarithms that are not of a common base

    with a calculator, use the CHANGE OF BASE FORMULA.

    log𝑎𝑀 = log𝑀

    log 𝑎 𝑜𝑟

    ln𝑀

    ln 𝑎

  • Change of Base Formula

    Evaluate the logarithm to 3 decimal places.

    S)log3 11 T)log2 9

    U)log6 40 V) log51 1

  • Write as a single log:

    CHALLENGE: Condense the logarithm completely

    log 𝑥 + 2 log 𝑦 − 3 log 𝑧 + 1

    2 log 5 − log 10 − 4 log𝑚

  • Expand:

    CHALLENGE: Expand the logarithm completely

    ln 5𝑥𝑦2𝑤

    6𝑧 1 3𝑚𝑛

  • OBJECTIVES

    • Understand properties of logarithms

    • Expand and condense logarithms

    • Evaluate logarithms without common bases (10,𝑒)

  • HOMEWORK

    In Class Assignment C11.3

    Homework H11.3

    EDPuzzle Q11.3