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Properties of Logarithms Quiz
46 Questions
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Properties of Logarithms Quiz

Created by
@SustainableAntigorite1088

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

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    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.

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