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Logarithm Properties

Total questions: 33

Worksheet time: 2hrs 12mins

Name
Class
Date
1.

Rewrite in exponential form:

log9 x = 2

a)

9x = 2

b)

2x = 9

c)

29 = x

d)

92 = x

2.

Rewrite in exponential form.

log3 a = 5

a)

5a = 3

b)

log35 = log3a

c)

a5 = 3

d)

35 = a

3.

Rewrite in Exponential Form:

log6 36 = 2

a)

26 = 36

b)

62 = 36

c)

362 = 6

d)

366 = 2

4.

Rewrite in logarithmic form.

25 = 32

a)

log25 = 32

b)

log322 = 5

c)

log232 = 5

d)

log532 = 2

5.

Rewrite logb (xn)

a)

n⋅logb x

b)

(logb x)n

c)

xn⋅logb x

d)

logb(xn)

6.

Solve for x.

5x = 1

a)

x = 0

b)

x = -1

c)

x = 2

d)

x = 1

7.

Rewrite in exponential form and solve for x.

log3 81 = x

a)

x = 2

b)

x = 3

c)

x = 4

d)

x = 5

8.

Rewrite in exponential form and solve for x.

log5 (25) = x

a)

x= 1/2

b)

x= 2

c)

x= 1

d)

x= - 2

9.

Rewrite in exponential form and then solve for x.

a)

x = 2,097,152

b)

x = 0.301

c)

x = 1.322

d)

x = 4.392

10.

Expand using log properties.

log (2c2)

a)

log 2 + 2⋅log c

b)

log 2 ⋅ log c2

c)

log 2 - 2⋅log c

d)

log 2 + log c2

11.

Expand using log properties

log (2 / 3)

a)

log 2 + log 3

b)

log 2 / log 3

c)

log 2 - log 3

d)

2/3 * log 1

12.

Expand using log properties.

log (a2)

a)

log a2

b)

2 log a

c)

log2 a

d)

loga 2

13.

Expand using log properties.

log (a2b4)

a)

2⋅log(a) + 4⋅log(b)

b)

4⋅log(a) + 2⋅log(b)

c)

log(a2) + log(b4)

d)

8(log(a) + log(b))

14.

Expand using log properties.

logb(xy)

a)

logbx + logby

b)

logbx - logby

c)

logbx ⋅ logby

d)

logbx / logby

15.

Expand using log properties.

logb(x/y)

a)

logbx - logby

b)

logbx + logby

c)

logbx ⋅ logby

d)

logbx / logby

16.
a)

6⋅log8(xyz)

b)

log8(x) - log8(y) - 6⋅log8(z)

c)

log8(x) + log8(y) - log8(z)

d)

log8(x) + log8(y) + 6⋅log8(z)

17.

Expand using log properties.

log(x²/y³)

a)

log x² + log y³

b)

2⋅log x + 3⋅log y

c)

log x + log y

d)

2⋅log x² +3⋅log y³

18.
a)
log (xy3)
b)
log (x6 − y3)
c)
log (x6/y3)
d)
log (x6 + y3)
19.

Condense using log properties.

log16 + log2 - log8

a)

log4

b)

log8

c)

log10

d)

log24

20.

Expand using log properties.

a)

log x + 5⋅log y

b)

5⋅log x + 5⋅log y

c)

5⋅log x - log y

d)

log x - 5⋅log y

21.

Expand using log properties.

a)

6⋅log8v - 2⋅log8u

b)

6⋅log8u - 2⋅log8v

c)

3⋅log8u - 2⋅log8v

d)

6⋅log8u + 2⋅log8v

22.

Condense using log properties. Simplify completely.

log5 3 + log5 6 + log5 9

a)

log5 69

b)

log5 56

c)

log5 162

d)

log5 98

23.

Condense using log properties. Simplify completely.

log 6 - log 3 + 2⋅log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

24.

Expand using log properties.

a)

A

b)

B

c)

C

d)

D

25.
a)
A
b)
B
c)
C
d)
D
26.

Condense using log properties. Simplify completely.

a)

A

b)

B

c)

C

d)

D

27.
Logarithmic functions are the inverse of...
a)
Linear Functions
b)
Exponential Functions 
c)
Quadratic Functions 
d)
Polynomial Functions 
28.

The common logarithm has what base?

a)

0

b)

10

c)

1

d)

2

29.

To expand a logarithm that uses division, we use what operation?

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Power

30.

To expand a logarithm that uses multiplication, we use what operation?

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

31.

To condense a logarithm that uses addition, we use what operation?

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

32.

To condense a logarithm that uses subtraction, we use ______________ and simplify completely.

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

33.

What rule is shown?

a)

Product Rule

b)

Quotient Rule

c)

Power Rule

d)

Common Base Property