4.2.1 Laws of Logarithms


4.2a Laws of Logarithms

  Law 1:   log a x y = log a x + log a y   Example:   log 5 25 x = log 5 25 + log 5 x   Beware!!   log a x + log a y log a ( x + y )   
  Law 2:   log a ( x y ) = log a x log a y      Example:   log 5 x 25 = log 5 x log 5 25   Beware!!   log a x y log a x log a y   
  Law 3:   log a x m = m log a x   Example:   log 5 y 5 = 5 log 5 y   Beware!!    ( log a x ) 2 2 log a x   


Example 1

Express the following in term of log a x   and log a y  .
(a) log a 3 x
(b) log a x 5
(c) log a y 5
(d) log a x y 3
(e) log a x 2 y
(f) log a y a 2 x 3

Law of Logarithms







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