# Properties of Logarithms

```NAME :
CLASS :
Properties of Logarithms
16 Questions
DATE :
1.
Write logb(xy) as two logs
A
logbx/logby
B
logbx+logby
C
logbx-logby
D
logbx*logby
2.
Write logb(x/y) as two logs
A
logbx*logby
B
logbx+logby
C
logbx/logby
D
logbx-logby
3.
Rewrite logb(xn)
A
logb(xn)
B
xnlogbx
C
nlogbx
D
(logbx)n
4.
Which property of logarithms is demonstrated below:
log9 20 =
​
log 20
log 9
​
A
Change of Base Property
B
Product property
C
Power property
D
Quotient property
5.
Use the properties of logarithms to retwrite
A
D
B
A
C
B
D
C
6.
Rewrite as a single logarithm:
log 3 + log 7
A
log 21
B
log 3/log 7
C
log 10
D
log 3/7
7.
Rewrite as a single logarithm:
log2 60 − log2 10
​
A
​
log2 60
log2 10
B
​
​
log2 6
​
​
C
8.
log2 70
D
​
log2 50
​
Use the properties of logarithms to rewrite as the sum of two logarithms:
log 55
A
log 40 + log 15
C
log 11 + log 5
9.
Use the properties of logarithms to rewrite as the difference of two logs:
B
log 50 + log 5
log5 45
​
A
log 45
log 5
C
log5 15 − log5 3
​
B
​
​
D
log5 50 − log5 5
​
​
log5 90 − log5 2
​
​
10.
Which of the logarithms below is equivalent to the following:
2 log 12
A
log 24
B
log 6
C
log 144
D
log 10
11.
Use the change of base rule to simplify. Round your answer to the nearest thousandth:
log4 20
​
12.
Use the change of base property to rewrite as a single logarithm:
log 15
log 3
​
A
log 5
B
log15 3
C
log3 15
D
log
B
True
B
False
B
True
​
13.
True or False:
log 12 - log 4 = log 8
A
False
14.
−2 log 3 = log
1
9
​
​
True or False:
A
15.
True
log 7
7
= log ( )
log 20
20
​
​
True or False:
A
False
1
5
​
16.
BONUS: Expand log6(5x3/y).
A
log65x3-log6y
C
log65+log6x3-log6y
B
log65+3log6x-log6y
```