8.4 Properties of Logarithms
Space isn't remote at all. It's only an hour's drive
away if your car could go straight upwards.
Review!
If y  b , then log b y  x
x
Write in logarithmic form: 81  34
Write in exponential form: log 2 64  6
Evaluate: log 25
1
625
Review: Properties of Exponents
a a  a
m
n
m n
m
a
mn
a
n
a
a 
m n
 a mn
Properties of Logarithms
For any positive numbers M , N , and
b, b  1 :
Product Property: log b MN  log b M  log b N
Quotient Property:
M
log b
 log b M  log b N
N
x
log
M
 x log b M
Power Property:
b
Name the property being used in each example:
log 5 2  log 5 13  log 5 26
Product Property
log 15  log 3  log 5
Quotient Property
7
7
7
2 log 3 5  log 3 4  log 3 100
Product Property & Power Property
Simplifying Logarithms
Write each logarithmic expression as a single logarithm
log 2 64  log 2 8
log 4 5  2 log 4 3
3 log 5 3  log 5 81
Can you write log 8 64  log 6 16 as a single logarithm?
Expanding Logarithms
Expand each logarithmic function
log 2 7b
 y
log  
3
2
3 5
log 7 a b
8.4 Properties of Logarithms
HW: Worksheet
Space isn't remote at all. It's only an hour's drive
away if your car could go straight upwards.