Evaluating logarithms using logarithm rules

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Introduction

Lessons

  1. A Summary of Logarithm Rules
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Examples

Lessons

  1. Select the correct answer:
    1. Which of the following correctly states the
      "product law"?
      i)
      log28+log24=log212 \log_2 8 + \log_2 4 = \log_2 12
      ii)
      log28+log24=log232\log_2 8 + \log_2 4 = \log_2 32
      iii)
      log28log24=log232\log_2 8 \cdot \log_2 4 = \log_2 32
    2. Which of the following correctly states the
      "quotient law"?
      i)
      logb15logb3=logb5\log_b 15 - \log_b 3 = \log_b 5
      ii)
      logb15logb3=logb12\log_b 15 - \log_b 3 = \log_b 12
      iii)
      logb8logb32=logb(14){{\log_b \sqrt{8}} \over {\log_b \sqrt{32}}} = \log_b(\sqrt{1 \over 4})
    3. Which of the following correctly states the
      "power law"?
      i)
      (log100)3=log1003(\log 100)^3 = \log 100^3
      ii)
      (log100)3=3log100(\log 100)^3 = 3\log 100
      iii)
      log1003=3log100\log 100^3 = 3\log 100
  2. Evaluate and state the laws involved in each step of
    the calculation:
    5log23805log2320{5 ^{log_2{^3}\sqrt{80}} \over 5 ^{log_2{^3}\sqrt{20}}}
    1. Express as a single logarithm:

      logA3logBlogC{\log A-3\log B-\log C}
      1. Evaluate logarithms:
        1. Determine the value of lognab2, {\log_n ab^2, }
          if logna=5{\log_na=5} and lognb=3{\log_nb=3}
        2. Given: log5x=y \log_5x = y
          ask:
          expresslog5125x4 \log_5125{x^4}
      2. Evaluate.
        1. log31512log35 \log_3 \sqrt{15}- {1\over2} \log_35
        2. (aloga8)(aloga3)aloga6\frac{({a^{\log_a8})}({a^{\log_a3}})}{a^{\log_a6}}
        1. If log3x2=2{\log_3x^2 = 2} and 2logbx=13,{2\log_b\sqrt{x} = {1\over3},}
          then the value of bb is ____________________ .
        2. If log5x2=4{\log_5x^2 = 4} and log2y3=6,{\log_2y^3 = 6 ,} and logbx+logby=12{\log_bx+\log_by = {1\over2}} where x, y > 0,
          then the value of b is ____________________ .

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