# MATH 1113 PreCalculus Section 5.5 notes Properties of Logarithms by axj70834

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```									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

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