Evaluating logarithms using logarithm rules

Lessons

• Introduction
  A Summary of Logarithm Rules

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• 1.
  Select the correct answer:
  
  a)

  Which of the following correctly states the
  "product law"?
  i)

  $\log_2 8 + \log_2 4 = \log_2 12$
  ii)

  $\log_2 8 + \log_2 4 = \log_2 32$
  iii)

  $\log_2 8 \cdot \log_2 4 = \log_2 32$
  
  
  
  b)

  Which of the following correctly states the
  "quotient law"?
  i)

  $\log_b 15 - \log_b 3 = \log_b 5$
  ii)

  $\log_b 15 - \log_b 3 = \log_b 12$
  iii)

  ${{\log_b \sqrt{8}} \over {\log_b \sqrt{32}}} = \log_b(\sqrt{1 \over 4})$
  
  
  
  c)

  Which of the following correctly states the
  "power law"?
  i)

  $(\log 100)^3 = \log 100^3$
  ii)

  $(\log 100)^3 = 3\log 100$
  iii)

  $\log 100^3 = 3\log 100$
  
  
  

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• 2.
  Evaluate and state the laws involved in each step of
  the calculation:
  

  ${5 \log_2{^3}\sqrt{80} \over 5 \log_2{^3}\sqrt{20}}$
  

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• 3.
  Express as a single logarithm:

  
  

  ${\log A-3\log B-\log C}$
  

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• 4.
  Evaluate logarithms:
  
  a)

  Determine the value of ${\log_n ab^2, }$
  if ${\log_na=5}$ and ${\log_nb=3}$
  
  
  b)

  Given: $\log_5x = y$
  ask:

  express$\log_5125{x^4}$
  
  
  

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• 5.
  Evaluate.
  a)

  $\log_3 \sqrt{15}- {1\over2} \log_35$
  
  
  
  b)

  $\frac{({a^{\log_a8})}({a^{\log_a3}})}{a^{\log_a6}}$
  
  
  

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• 6.
  a)

  If ${\log_3x^2 = 2}$ and ${2\log_b\sqrt{x} = {1\over3},}$
  then the value of $b$ is ____________________ .
  
  
  
  b)

  If ${\log_5x^2 = 4}$ and ${\log_2y^3 = 6 ,}$ and ${\log_bx+\log_by = {1\over2}}$ where x, y > 0,
  then the value of b is ____________________ .
  
  
  

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