Combining product rule and quotient rule in logarithms

Combining product rule and quotient rule in logarithms

Lessons

log[AB÷C÷DE]=logA+logBlogClogD+logE \log [A \cdot B \div C \div D \cdot E] = \log\;A + \log\;B - \log\;C - \log\;D + \log\;E
  • 1.
    Evaluate:
    a)
    log560log53+log55log520\log_5 60 - \log_5 3 + \log_5 5 - \log_5 20

    b)
    given:
    abc=9 {{a \over {bc}} = 9}
    ask: 5log3a5log3b5log3c 5\log_3 a - 5\log_3 b - 5\log_3 c

    c)
    if logax=3 \log_a x = 3 and logay=4, \log_a y = 4,
    evaluate (loga1xy)2 (\log_a {1 \over xy})^2


  • 2.
    Simplify log5a3logb2+log2bc+logbloga3100 \log 5a^3 - \log b^2 + \log {2b \over c} + \log b - \log{a^3 \over 100}