Evaluating logarithms using logarithm rules

Evaluating logarithms using logarithm rules

Lessons

  • 1.
    Select the correct answer:
    a)
    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

    b)
    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})

    c)
    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}}

  • 3.
    Express as a single logarithm:

    logA3logBlogC{\log A-3\log B-\log C}

  • 4.
    Evaluate logarithms:
    a)
    Determine the value of lognab2, {\log_n ab^2, }
    if logna=5{\log_na=5} and lognb=3{\log_nb=3}

    b)
    Given: log5x=y \log_5x = y
    ask:
    expresslog5125x4 \log_5125{x^4}


  • 5.
    a)
    log31512log35 \log_3 \sqrt{15}- {1\over2} \log_35

    b)
    (aloga8)(aloga3)aloga6\frac{({a^{\log_a8})}({a^{\log_a3}})}{a^{\log_a6}}


  • 6.
    a)
    if log3x2=2{\log_3x^2 = 2} and 2logbx=13,{2\log_b\sqrt{x} = {1\over3},}
    then the value of bb is ____________________ .

    b)
    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 ____________________ .