Combining product rule and quotient rule in logarithms

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  1. Evaluate:
    1. logโก560โˆ’logโก53+logโก55โˆ’logโก520\log_5 60 - \log_5 3 + \log_5 5 - \log_5 20
    2. given:
      abc=9 {{a \over {bc}} = 9}
      ask: 5logโก3aโˆ’5logโก3bโˆ’5logโก3c 5\log_3 a - 5\log_3 b - 5\log_3 c
    3. if logโกax=3 \log_a x = 3 and logโกay=4, \log_a y = 4,
      evaluate (logโกa1xy)2 (\log_a {1 \over xy})^2
  2. Simplify logโก5a3โˆ’logโกb2+logโก2bc+logโกbโˆ’logโกa3100 \log 5a^3 - \log b^2 + \log {2b \over c} + \log b - \log{a^3 \over 100}
    Topic Notes
    logโก[Aโ‹…BรทCรทDโ‹…E]=logโกโ€…โ€ŠA+logโกโ€…โ€ŠBโˆ’logโกโ€…โ€ŠCโˆ’logโกโ€…โ€ŠD+logโกโ€…โ€ŠE \log [A \cdot B \div C \div D \cdot E] = \log\;A + \log\;B - \log\;C - \log\;D + \log\;E