Properties of Logarithms Quiz

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

Expand 4log(2) - log(5)

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

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

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

Expand log(x) - 6log(y)

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

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

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

Expand 4log(x) - log(y)

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

Expand log(x) - 5log(y)

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

Condense log(3) - log(8)

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

Condense (log(6))/3

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

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

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

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

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

Condense log(7) - 2log(12)

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

Condense (2log(7))/3

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

Condense 6log₃(x) + 6log₃(y)

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

Condense log₄(x) - 6log₄(y)

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

Condense log₃(x/y⁵)

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

Condense log₆(x²⁰y⁵)

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

Condense log₃(x⁴/y²⁰)

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

Condense (log(x))/2

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

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

<p>log(4x²/75y²) (A)</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

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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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