Free Printable Log and Exponential quiz Reivew

1.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

2.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

3.

$\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

4.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

5.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

6.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

7.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

8.

Condense: log16 + log2 - log8

a)

log4

b)

log8

c)

log10

d)

log24

9.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

10.

Rewrite log_x95 = 2.3

a)

x^2.3 = 95

b)

95^2.3 = x

c)

2.3⁹⁵ = x

d)

x⁹⁵= 2.3

11.

Without a calculator, evaluate log₄1

a)

¹/₄

b)

0

c)

-1

d)

not possible

12.

Without a calculator, evaluate log₁₂₅ 25

a)

²/₃

b)

³/₂

c)

¹/₆

d)

¹/₅

13.

Without a calculator, evaluate log₆ -36

a)

not possible

b)

-2

c)

2

d)

¹/2

14.

$Evaluate\ \log_28$

(a)

15.

$Evaluate\ \log_864$

(a)

16.

$Evaluate\ \log_77$

(a)

17.

$Evaluate\ \log_{10}1000$

(a)

18.

$Evaluate\ \log_8\frac{1}{8}$

(a)

19.

$Evaluate\ \log_5\sqrt{5}$

(a)

20.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

21.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

22.

Rewrite as an exponential: $\log_7\left(\frac{1}{49}\right)=-2$

a)

$7^{\frac{1}{49}}=-2$

b)

$\left(\frac{1}{49}\right)^{-2}=7$

c)

$7^{-2}=\frac{1}{49}$

d)

$\left(-2\right)^7=\frac{1}{49}$

23.

Rewrite as an exponential: $\log_93=\frac{1}{2}$

a)

$9^{\frac{1}{2}}=3$

b)

$3^{\frac{1}{2}}=9$

c)

$9^3=\frac{1}{2}$

d)

$\left(\frac{1}{2}\right)^9=3$

24.

Solve for x:

\log_x\sqrt{6}=\frac{1}{2}

*Hint: Rewrite as an exponential first.

(a)

25.

Condense into a single log:

log 6 + log 4

(a)

26.

Condense into a single log:

\log_320-\log_35

a)

$\log_315$

b)

$\log_34$

c)

$\log_3100$

d)

$\log_3\frac{1}{4}$

27.

Rewrite with no coefficient:

3\log2

(a)

28.

Condense into a single log:

2\log7+5\log x-2\log5

a)

$\log\left(\frac{49x^5}{25}\right)$

b)

$\log\left(\frac{49x^5}{10}\right)$

c)

$\log\left(\frac{14x^5}{25}\right)$

d)

$\log\left(\frac{14x^5}{10}\right)$

29.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

30.

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

31.

Re-Write the Logarithm Equation into Exponential Form
log_hw = d

a)

w = h^d

b)

w^d = h

c)

h = w^d

d)

h^w = d

32.

What is the x-intercept of log₇(x)?

a)

Pizza

b)

-1

c)

0

d)

1

33.

Match the graph with its equation

a)

y = log₆(-x) + 1

b)

y = log₆(x − 2) + 1

c)

y = log₆(x + 2) - 1

d)

y = log(x-8) + 1

34.

Logarithms and Exponentials are what?

a)

parallel

b)

perpendiular

c)

inverses

d)

congurent

35.

Match the graph with its equation

a)

y = log₅ (x + 1) + 1

b)

y = log₅ (x - 1) + 1

c)

y = log₅ (x²) + 1

d)

y = log₅ (x)-1

36.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

[0, ∞)

c)

(0, ∞)

d)

Pickle

37.

What are the transformations of this graph?

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

38.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

39.

Where is the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

40.

Match the graph with its equation

a)

y = log₅ (x + 1) + 1

b)

y = log₅ (x - 1) + 1

c)

y = log₅ (x²) + 1

d)

y = log₅ (x)-1

41.

Pick the equation that matches the graph

a)

A

b)

B

c)

C

d)

D

42.

Describe the transformations of f(x)= -log₂(x+1)

a)

left 1

b)

left one & over the y-axis

c)

left one & over the x-axis

d)

right one & over the x axis

43.

Find the domain and range of:
f(x) = log₂(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

44.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

45.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

46.

Which graph best represents the following logarithmic function?
$y=\log_4x$

a)

b)

c)

d)

47.

Using the parent function $y=\log_3x$ what would the graph of $y=\log_3\left(x+5\right)$ look like?

a)

Horizontal shift left 5 units

b)

Horizontal shift right 5 units

c)

Vertical shift up 5 units

d)

Vertical shift down 5 units

48.

Find the corresponding graph of
$\log_3\left(x-1\right)+4$

a)

b)

c)

d)

49.

What is the change in the graphs from f(x) to g(x)?

f\left(x\right)=\log_8x

to

g\left(x\right)=\log_8\left(x+9\right)-7\

a)

Right nine and down seven

b)

Left nine and down seven

c)

Left nine and up seven

d)

Right nine and up seven

50.

Describe the transformations from the parent function y=log₆x to y = - log ₆ (x - 1) - 5

a)

Reflection about the x-axis; shift left one and up five

b)

Reflection about the x-axis; shift left one and down five

c)

Reflection about the y-axis; shift right one and down five

d)

Reflection about the x-axis; shift right one and down five

51.

What is the domain of y=2^x?

a)

x>0

b)

x=all real numbers

c)

y>0

d)

y=all real numbers

52.

What is the range of y=2^x?

a)

x>0

b)

x=all real numbers

c)

y>0

d)

y=all real numbers

53.

Evaluate: ln e^2x

a)

e

b)

ln x

c)

2x

d)

2

54.

Evaluate: log_aa^-8

a)

a

b)

5

c)

-8

d)

3

55.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

56.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

57.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

58.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

59.

Is this exponential growth or decay?

a)

Growth

b)

Decay

60.

What is the initial value for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

61.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

62.

What is b, the common ratio, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

63.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

64.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

65.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

66.

Use the change of base rule to rewrite this problem:

log₃64

a)

log(64)/log(3)

b)

log(3)/log(64)

67.

Change $\log_{12}⁡2$ into the form of $\frac{\log⁡a}{\log b}$ , where $a$ and $b$ are integers

a)

$\frac{\log12}{\log2}$

b)

$\frac{\log⁡2}{\log12}$

68.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

69.

Where does Ariel want to be?

a)

On a cruise

b)

Queen of the sea

c)

In her treasure trove

d)

Where the people are

70.

How much water can an elephant hold in its trunk at one time?

a)

4 cups

b)

12 teaspoons

c)

2 gallons

d)

85 tablespoons

71.

There are 8 brothers in the family. Each of them has a sister. How many children are there in the family?

a)

16

b)

15

c)

9

d)

10

72.

Name the world's biggest island.

a)

Hawaii

b)

Greenland

c)

Pacific island

d)

Australia

Log and Exponential quiz Reivew

Total questions: 72

Worksheet time: 3hrs 0mins

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