MAC 1105
5.4 Properties of Logarithms
log a a  1
log a  a x   x
log a 1  0
aloga x  x
log a (MN )  log a M  log a N
M
log a 
N

  log a M  log a N

log a  M p   p log a M
change-of-base formula: log a M 
logb M
logb a
Express in terms of sums and differences of logarithms. Use all possible properties (except
change of base) to obtain the final form.
1)
8)
√
9)
√
5)
2)
( )
3)
4)
log (0.0001)
6)
( )
7)
√
Express as a single logarithm and, if possible, simplify.
10)
11)
√
12)
13)
14)
Given that log a (2)  0.301 , log a (3)  0.477 , log a (7)  0.845 , find each of the following, if
possible. Round your answer to the nearest thousandth, if necessary.
15)
( )
16)
17)
Simplify.
20)
18)
19)