N 11-2
Laws of Logarithms:
Expanding and Condensing Log Expressions
Let b be the base of a logarithmic function (b  0, b  1) .
Let M and N be positive numbers or variables.
1. logb MN = logbM + logbN
2. logb
M
 logb M  logb N
N
3. logbMk = k•logbM
Product Property
NOTE: The BASE
stays the same when
using these laws. Any
change of base
requires the use of the
“change of base”
formula.
Quotient Property
Power Property
Use the laws of logarithms to expand the following expressions.
1. log2 5ab =
2. log5
8
=
x
3. log2 6 x 2 y 3 =
4a2
4. log3
=
bc 2
N 11-2
a5
5. log
=
b
(NOTE: What power does a
square root radical represent?)
Use the laws of logarithms to condense the following expressions.
6. log57 + 3 log5x =
7. log2x – log23 =
8.
1
log6M – 3log6N =
2
9. 3 (log2a – log2b) =
10. log34 + 3log3M – 2 log3N =