4. 2 Properties of Logarithms
Logarithm Properties
Definition of logs:
Ex:
Product Property:
Ex:
Quotient Property:
( )
Ex:
( )
Power Property:
Ex:
Inverse relationship:
Ex:
Problem 1:
Write each expression as a single logarithm. Then simplify, if possible.
a)
b)
4. 2 Properties of Logarithms
Problem 2
Use the properties of logarithms to write each single logarithm as a sum or difference of logarithms.
Then simplify, if possible.
a)
(
)
b)
Problem 3
Solve for x and check your answers!!!
a)
b)
c)
4. 2 Properties of Logarithms
More Practice Problems
Write each equation in logarithmic form:
1) 19 2  361
1
2)  
4
3
 64
3) 20 3  8000
Write each equation in exponential form:
4) log 5 15,625  6
5) log 11
1
 4
14,641
6) log 1 625  4
5
Solve each equation for x. Round your answers to the nearest hundredth.
7) 10 x  35
1
10)  
2
8) 10 x  1055
9) 5 x  16
x
 17
11) 4.22 2 x  61
Find the value of v in each equation:
12) v  log 15 225
13)  4  log 5 v
14) log v
1
 4
256
Write each expression as a sum or a difference of logarithms. Then simplify, if possible.
4. 2 Properties of Logarithms
15) log 8
64
y
16) log 7 (5 x 2 y 3 )
Write each expression as a single logarithm. Then simplify, if possible.
17) log b m  log b 2  log b x
18) 3 log b x  (log b 4  log b x)
19)
20)
Solve for x and check your answers!!!
21)
22)
23)
24)
25)
26)
27)
28)