MATH 1113 PreCalculus Section 5.5 notes Properties of Logarithms

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MATH 1113 PreCalculus Section 5.5 notes Properties of Logarithms Powered By Docstoc
					MATH 1113                                     PreCalculus                            Section 5.5 notes

Properties of Logarithms
1) Show that log a 1 = 0                                     Show that log a a = 1




2) a log a M = M                                             a) 2 log 2 π = ____________
                                                             b) log 0.2 0.2 − 2 = __________
   log a a r = r
                                                             b) ln e kt = ____________


3) log a ( MN ) = ________________________
         M   
4) log a      = _________________________
         N   
5) log a M r = _________________

1) Write log 2 ( x 2 3 x − 1), x > 1 as a sum of logarithms. Express all powers as factors by using property 5.




                        x4
2) Write log 6                  as a sum and/or difference of logarithms. Express all powers as factors by using
                   ( x 2 + 3) 2
property 5.




              x3 x − 2
3) Write ln               , x > 2 as a sum and/or difference of logarithms. Express all powers as factors.
               ( x + 1) 2
  Write each of the following as a single logarithm.
  ( a ) 3ln 2 + ln ( x 2 ) + 2
         1
  (b )     log a 4 − 2 log a 5
         2

  ( c ) − 2 log a 3 + 3log a 2 − log a ( x 2 + 1)



More properties
       If M = N, then log a M = log a N
       If log a M = log a N , then M = N

Approximate the following: log 3 12 using one of the above properties




One more property
                          log b M
              log a M =
                           log b a

1) Solve log 5 89 by hand and by using this formula.




2) Approximate log         2
                                 5




                                                                        5.5 Assignment
                                                                        1-6All, 7-19Odd,
                                                                        23-67Odd, 79-83Odd