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Logarithms2

Total questions: 40

Worksheet time: 20mins

Name
Class
Date
1.
Write as one logarithm. Simplify, if possible.
log39 + log327
a)
-1
b)
5
c)
4
d)
1
2.
Write as one logarithm. Simplify, if possible.
log2800 - log2100
a)
8
b)
3
c)
-3
d)
1
3.
Write as one logarithm. Simplify, if possible.
log5125 - log525
a)
1
b)
0
c)
5
d)
-1
4.
Write as one logarithm. Simplify, if possible.
log63 + log62
a)
0
b)
log65
c)
log61
d)
1
5.
Evaluate.
log381
a)
4
b)
1/4
c)
-4
d)
-1/4
6.
Evaluate.
log6(1/216)
a)
3
b)
1/3
c)
-1/3
d)
-3
7.
Evaluate.
3 log24
a)
3
b)
6
c)
2
d)
4
8.
Evaluate.
3 log82
a)
1/3
b)
3
c)
1
d)
9
9.
Write in logarithmic form.
52 = 25
a)
log52 = 25
b)
log225 = 5
c)
log255 = 2
d)
log525 = 2
10.
Write in logarithmic form.
2-4 = 1/16
a)
log2(1/16) = -4
b)
log-4(1/16) = 2
c)
log -4 2 = 1/16
d)
log2(-4) = 1/16
11.
Write in exponential form.
log232 = 5
a)
2-5 = 32
b)
232 = 5
c)
25 = 32
d)
325 = 2
12.
Write in exponential form.
log2(1/8) = -3
a)
2-3 = 1/8
b)
21/8 = -3
c)
-32 = 1/8
d)
-31/8 = 2
13.

Evaluate the following logarithm:


log327

a)

3

b)

2

c)

-3

d)

1/3

14.

Evaluate the following logarithm:


log55

a)

1

b)

0

c)

-1

d)

1/2

15.

Evaluate the following logarithm:


log33

a)

1

b)

0

c)

-1

d)

1/2

16.

Evaluate the following logarithm:


log416

a)

1

b)

-2

c)

2

d)

1/2

17.

Evaluate the following logarithm:


log42

a)

-1/2

b)

-2

c)

2

d)

1/2

18.

Evaluate the following logarithm:


log8√8

a)

-1/2

b)

-1

c)

1

d)

1/2

19.

Evaluate the following logarithm:


log2√2

a)

-1/2

b)

-1

c)

1

d)

1/2

20.

Evaluate the following logarithm:


log250.2

a)

-1/2

b)

-2

c)

2

d)

1/2

21.

Evaluate the following logarithm:


log40.5

a)

-1/2

b)

-2

c)

2

d)

1/2

22.

Evaluate the following logarithm:


log121

a)

1

b)

0

c)

-1

d)

1/2

23.

Evaluate the following logarithm:


log151

a)

1

b)

0

c)

-1

d)

1/2

24.

Evaluate the following logarithm:


log3(1/3)

a)

-2

b)

-1/2

c)

-1

d)

1/2

25.

Evaluate the following logarithm:


log4(1/64)

a)

3

b)

-1/3

c)

-3

d)

1/3

26.

Evaluate the following logarithm:


log273

a)

1/3

b)

-3

c)

-1/2

d)

1/2

27.

Evaluate the following logarithm:


log84

a)

2/3

b)

3/2

c)

3/4

d)

1/2

28.

Evaluate the following logarithm:


log25125

a)

2/3

b)

3/2

c)

3/4

d)

1/2

29.

Evaluate the following logarithm:


log8127

a)

2/3

b)

3/2

c)

3/4

d)

4/3

30.

Evaluate the following logarithm:


log1632

a)

4/3

b)

3/4

c)

5/4

d)

4/5

31.

Evaluate the following logarithm:


log636

a)

3

b)

2

c)

1

d)

0

32.

Evaluate the following logarithm:


log66

a)

3

b)

2

c)

1

d)

0

33.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
34.
Write logb(x/y) as two logs
a)
logbx-logby
b)
logbx+logby
c)
logbx*logby
d)
logbx/logby
35.
Rewrite logb(xn)
a)
nlogbx
b)
(logbx)n
c)
xnlogbx
d)
logb(xn)
36.
a)
24log(u) - log(v)
b)
24log(u) + 6log(v)
c)
4log(u) + 6log(v)
d)
4log(u) - 6log(v)
37.
a)
60 log(ab)
b)
6log(a) + log(b)
c)
log(a) - 30 log(b)
d)
6log(a) + 30 log(b)
38.

Rewrite log28 = 3 in exponential form

a)

28 = 3

b)

23 = 8

c)

32 = 8

d)

83 = 2

39.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
40.

Write in logarithmic form

2-4 = 1/16

a)

log2(1/16) = -4

b)

log-4(1/16) = 2

c)

log -4 2 = 1/16

d)

log2(-4) = 1/16

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