Properties of Logarithms Quiz
46 Questions
100 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Expand log(6) + log(11)

  • log(6) - log(11)
  • log(6/11)
  • log(6⋅11) (correct)
  • log(6) + log(11)

    • Expand log(5) + log(3)

  • log(5⋅3) (correct)
  • log(5/3)
  • log(15)
  • log(5) + log(3)

    • Expand 5log(6) - 5log(11)

  • log(6/11)⁵ (correct)
  • 5(log(6) - log(11))
  • log(6) - log(11)
  • log(6/11)

    • Expand log(3) + 3log(2)

    <p>log(3⋅2³)</p> Signup and view all the answers

    Expand 4log(2) - log(5)

    <p>log(2⁴/5)</p> Signup and view all the answers

    Expand 6log(6) - 6log(5)

    <p>log(6/5)⁶</p> Signup and view all the answers

    Expand log(x) - 6log(y)

    <p>log(x/y⁶)</p> Signup and view all the answers

    Expand 2log(x) + 2log(y)

    <p>log(x⋅y)²</p> Signup and view all the answers

    Expand 4log(x) - log(y)

    <p>log(x⁴/y)</p> Signup and view all the answers

    Expand log(x) - 5log(y)

    <p>log(x/y⁵)</p> Signup and view all the answers

    Expand (1/3)log(x) + (1/3)log(y) + (1/3)log(z)

    <p>log(³√x⋅y⋅z)</p> Signup and view all the answers

    Condense log(3) - log(8)

    <p>log(3/8)</p> Signup and view all the answers

    Condense (log(6))/3

    <p>log(³√6)</p> Signup and view all the answers

    Condense 4log(3) - 4log(8)

    <p>log(3⁴/8⁴)</p> Signup and view all the answers

    Condense log(2) + log(11) + log(7)

    <p>log(154)</p> Signup and view all the answers

    Condense log(7) - 2log(12)

    <p>log(7/12²)</p> Signup and view all the answers

    Condense (2log(7))/3

    <p>log(³√7²)</p> Signup and view all the answers

    Condense 6log₃(x) + 6log₃(y)

    <p>log₃(x⁶y⁶)</p> Signup and view all the answers

    Condense log₄(x) - 6log₄(y)

    <p>log₄(x/y⁶)</p> Signup and view all the answers

    Condense log₃(x/y⁵)

    <p>log₃(x) - 5log₃(y)</p> Signup and view all the answers

    Condense log₆(x²⁰y⁵)

    <p>20log₆(x) + 5log₆(y)</p> Signup and view all the answers

    Condense log₃(x⁴/y²⁰)

    <p>4log₃(x) - 20log₃(y)</p> Signup and view all the answers

    Condense (log(x))/2

    <p>log(√x)</p> Signup and view all the answers

    Condense 2(log(2x) - log(y)) - (log 3 + 2log(5))

    <p>log(4x²/75y²)</p> Signup and view all the answers

    Approximate log₃(3.3)

    <p>1.087</p> Signup and view all the answers

    Approximate log₂(30)

    <p>4.907</p> Signup and view all the answers

    Approximate log₄(5)

    <p>1.161</p> Signup and view all the answers

    Approximate log₂(2.1)

    <p>1.07</p> Signup and view all the answers

    Approximate log(3.55)

    <p>0.55</p> Signup and view all the answers

    Approximate log₆(13)

    <p>1.432</p> Signup and view all the answers

    Approximate log₆(40)

    <p>2.059</p> Signup and view all the answers

    Approximate log₄(3.5)

    <p>0.904</p> Signup and view all the answers

    Approximate log₂(2.9)

    <p>1.536</p> Signup and view all the answers

    Approximate log₆(22)

    <p>1.725</p> Signup and view all the answers

    Approximate log₇(8.7)

    <p>1.112</p> Signup and view all the answers

    Approximate log₃(62)

    <p>3.757</p> Signup and view all the answers

    Approximate log₈(4)

    <p>0.667</p> Signup and view all the answers

    Approximate log₂(8.7)

    <p>3.121</p> Signup and view all the answers

    Approximate log₉(71)

    <p>1.94</p> Signup and view all the answers

    Approximate log₁₃(194)

    <p>2.054</p> Signup and view all the answers

    Approximate log₁₃(12.9)

    <p>0.997</p> Signup and view all the answers

    Approximate log₅(10.818)

    <p>1.48</p> Signup and view all the answers

    Approximate log₃(189)

    <p>4.771</p> Signup and view all the answers

    Approximate log₁₆(194)

    <p>1.9</p> Signup and view all the answers

    Approximate log₅(183)

    <p>3.237</p> Signup and view all the answers

    Approximate log₁₄(2.6)

    <p>0.362</p> Signup and view all the answers

    Study Notes

    Properties of Logarithms

    • log(a) + log(b) expands to log(ab)
    • log(a) - log(b) expands to log(a/b)
    • n * log(a) expands to log(a^n)
    • Logarithm of a product: log(xy) = log(x) + log(y)
    • Logarithm of a quotient: log(x/y) = log(x) - log(y)
    • Logarithm of a power: log(a^b) = b * log(a)

    Specific Expansions and Condensations

    • log(6) + log(11) condenses to log(66)
    • log(5) + log(3) condenses to log(15)
    • 5log(6) - 5log(11) condenses to log((6/11)⁵)
    • log(3) + 3log(2) condenses to log(24)
    • 4log(2) - log(5) condenses to log(16/5)
    • 6log(6) - 6log(5) condenses to log((6/5)⁶)
    • log(x) - 6log(y) condenses to log(x/y⁶)
    • 2log(x) + 2log(y) condenses to log((xy)²)
    • 4log(x) - log(y) condenses to log(x⁴/y)
    • log(x) - 5log(y) condenses to log(x/y⁵)
    • (1/3)log(x) + (1/3)log(y) + (1/3)log(z) condenses to log(³√(xyz))
    • log(x) + log(y) + 2log(z) condenses to log(xyz²)

    Logarithmic Approximations

    • Approximations utilize logarithms based on specific values
    • log₃(3.3) ≈ 1.087
    • log₂(30) ≈ 4.907
    • log₄(5) ≈ 1.161
    • log₂(2.1) ≈ 1.07
    • log(3.55) ≈ 0.55
    • log₆(13) ≈ 1.432
    • log₆(40) ≈ 2.059
    • log₄(3.5) ≈ 0.904
    • log₂(2.9) ≈ 1.536
    • log₆(22) ≈ 1.725
    • log₇(8.7) ≈ 1.112
    • log₃(62) ≈ 3.757
    • log₈(4) ≈ 0.667
    • log₂(8.7) ≈ 3.121
    • log₉(71) ≈ 1.94
    • log₁₃(194) ≈ 2.054
    • log₁₃(12.9) ≈ 0.997
    • log₅(10.818) ≈ 1.48
    • log₃(189) ≈ 4.771
    • log₁₆(194) ≈ 1.9
    • log₅(183) ≈ 3.237
    • log₁₄(2.6) ≈ 0.362

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Test your understanding of the properties and specific expansions of logarithms through various equations and examples. This quiz covers key logarithmic principles including addition, subtraction, and power rules, alongside practical applications and approximations. Perfect for students learning about logarithms in algebra or mathematics.

    More Like This

    Logarithmic Equations and Properties Quiz
    3 questions

    Logarithmic Equations and Properties Quiz

    ReliableForest avatar
    ReliableForest
    Properties and Functions of Logarithms
    9 questions

    Properties and Functions of Logarithms

    SpellboundBohrium avatar
    SpellboundBohrium
    Exponents and Logarithms
    10 questions

    Exponents and Logarithms

    ExceptionalQuasimodo avatar
    ExceptionalQuasimodo
    Funciones Logarítmicas y Propiedades
    11 questions

    Funciones Logarítmicas y Propiedades

    ThumbsUpSiren avatar
    ThumbsUpSiren
    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser