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Combining product rule and quotient rule in logarithms

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Lessons
  1. Evaluate:
    1. log⁡560−log⁡53+log⁡55−log⁡520\log_5 60 - \log_5 3 + \log_5 5 - \log_5 20
    2. given:
      abc=9 {{a \over {bc}} = 9}
      ask: 5log⁡3a−5log⁡3b−5log⁡3c 5\log_3 a - 5\log_3 b - 5\log_3 c
    3. if log⁡ax=3 \log_a x = 3 and log⁡ay=4, \log_a y = 4,
      evaluate (log⁡a1xy)2 (\log_a {1 \over xy})^2
  2. Simplify log⁡5a3−log⁡b2+log⁡2bc+log⁡b−log⁡a3100 \log 5a^3 - \log b^2 + \log {2b \over c} + \log b - \log{a^3 \over 100}