Free Printable Logarithm 2

1.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

2.

a)

A

b)

B

c)

C

d)

D

3.

Evaluate log₇ 343

a)

3

b)

49

c)

7

d)

1

4.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

5.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

6.

Write the expression as a single logarithm. Then simplify if possible.

log₅3 + log₅6 - log₅9

a)

log₅0

b)

log₅56

c)

log₅2

d)

log₅98

7.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

8.

Write the logarithm expression as a single logarithm

log₅4 + log₅3

a)

log₅7

b)

log₅12

c)

log₇5

d)

3log₅4

9.

Expand the logarithm expression

log₅5x^-5

a)

-5(log₅5x)

b)

-5log₅5 + log₅x

c)

log₅25x

d)

1 - 5log₅x

10.

Evaluate log₂√2

a)

-2

b)

2

c)

1

d)

1/2

11.

(log a)(log b) = log (a+b)

a)

True

b)

False

12.

Given log₁₂1= x. Find x

a)

1

b)

0

c)

12

d)

-1

13.

a)

A

b)

B

c)

C

d)

D

14.

Expand

a)

log₈x+log₈y+log₈z

b)

5log₈x+5log₈y+5log₈z

c)

log₈xy+5log₈z

d)

log₈x+log₈y+5log₈z

15.

Condense

a)

A

b)

B

c)

C

d)

D

16.

Expand log₆(5x³/y).

a)

log₆5x³-log₆y

b)

log₆5+log₆x³-log₆y

c)

log₆5+3log₆x-log₆y

17.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

18.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

19.

Write as one logarithm. Simplify, if possible.
log₂800 - log₂100

a)

8

b)

3

c)

-3

d)

1

20.

Evaluate.
3 log₈2

a)

¹/₃

b)

3

c)

1

d)

9

21.

What is the Vertical Asymptote?

a)

x=5

b)

x=0

c)

y=0

d)

x=1

22.

What is the Domain?

a)

x > 0

b)

All Real Numbers

c)

x > 1

d)

x < 1

23.

What is the Range?

a)

y > 0

b)

All Real Numbers

c)

y > 1

d)

y < 1

24.

What is the Domain?

a)

x > -3

b)

x > 5

c)

x > 3

d)

x > -5

25.

Expand the logarithm
log₇ x³/y⁴

a)

log₇ x³ - log₇ y⁴

b)

log₇ x³ + log₇ y⁴

c)

3log₇ x - 4log₇ y

d)

(3log₇ x) / (4log₇ y⁾

26.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

27.

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3

a)

b)

c)

d)

28.

Which graph matches the logarithmic equation

a)

b)

c)

d)

29.

Which graph is logarithmic

a)

b)

c)

d)

30.

Describe domain of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

31.

What kind of asymptotes do logs have?

a)

horizontal ( y=0)

b)

vertical (x=0)

32.

Find the domain and range of:
f(x) = ln(x)

a)

D: all real numbers
R: y > 0

b)

Domain: all real numbers
Range: all real numbers

c)

Domain: x > 0
Range: all real numbers

d)

Domain: all real numbers
Range: y < 0

33.

f(x)=log₅(x+4) - 2

Find the Domain and Range

a)

Domain: x ≥ -4

Range: all real numbers

b)

Domain: all real numbers

Range: y ≥ -4

c)

Domain: all real numbers

Range: y > -4

d)

Domain: x > -4

Range: all real numbers

34.

a)

A

b)

B

c)

C

d)

D

35.

log (x) + log (x) = log (25)

a)

-5, 5

b)

5

c)

-5

d)

25

36.

Solve: 2^3x = 15

a)

2.3

b)

-2.3

c)

1.3

d)

-1.3

37.

Simplify the expression
log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

38.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

39.

Condense

a)

A

b)

B

c)

C

d)

D

40.

Evaluate the following logarithm by converting to exponential form.
log_⅕125 = x

a)

x = 3

b)

x = -3

c)

x = 25

d)

x = 5

41.

Graph $y\ =\log_7x$

a)

b)

c)

d)

42.

Graph $\log_7\left(x+2\right)$

a)

b)

c)

d)

43.

What is the equation of the graph?

a)

$y=\log_4\left(x-2\right)+1$

b)

$y=\log_4\left(x+2\right)-1$

c)

$y=\log_4\left(x-2\right)-1$

d)

$y=\log_4\left(x+2\right)+1$

44.

Which function has a horizontal asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

45.

How are exponentials and logarithms related?

a)

They're cousins

b)

They're inverses

c)

They're not related

d)

They're reciprocals

Logarithm 2

Total questions: 45

Worksheet time: 44mins

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