Free Printable Unit 4 Logs/Exps Test Review

1.

Logarithms and Exponentials are what?

a)

parallel

b)

perpendiular

c)

inverses

d)

congurent

2.

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

3.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

4.

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

5.

Identify the asymptote for the graph

f(x) = -2 (3)^{x + 4}- 8

a)

y = -4

b)

y = -8

c)

x = -8

d)

x = - 4

6.

What is the equation of the graph shown, and what is the y-intercept?

a)

y = -4 (2)^x ; a = 4

b)

y = 2 (4)^x ; a = 2

c)

y = -2 (4)^x ; a = 4

d)

y = -2 (4)^x ; a = -2

7.

What is the domain and range?

Choose ALL that apply

a)

Domain: (-∞, ∞)

b)

Domain: (-3, ∞)

c)

Domain: (3, ∞)

d)

Range: (-∞, ∞)

e)

Range: (5, ∞)

8.

List the transformations.

Choose ALL that apply

f(x) = -2 (3)^{x - 5} + 7

a)

Left 5

b)

Right 5

c)

Up 7

d)

Down 7

e)

Reflection

9.

Write an exponential function to model the situation. Solve.

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. What will the cost be after 4 years?

y = a(1 + r)^t

a)

C(t) = 12000(1.06)^t ; $3149.72

b)

C(t) = 12000(.06)^t ; $3149.72

c)

C(t) = 12000(.06)^t ; $1472.95

d)

C(t) = 12000(1.06)^t ; $15149.72

10.

Write an exponential function to model the situation. Solve.

You invest $1500 at a rate of 3.5% compounded annually. What will the balance be after 4 years?

A = P(1+r/n)^nt

a)

B(t) = 1500(1.035)^t ; $221.28

b)

B(t) = 1500(1.035)^t ; $1721.28

c)

B(t) = 1500(.035)^t ; $221.28

d)

B(t) = 1500(1.035)^t ; $1628.85

11.

Write an exponential function to model the situation. Solve.

The value of a car is $18000 and is depreciating at a rate of 12% per year. What will the value of the car be after 10 years?

y = a(1 - r)^t

a)

V(t) = 18000(.88)^t ; $12986.98

b)

V(t) = 18000(.12)^t ; $12986.98

c)

V(t) = 18000(.88)^t ; $5013.02

d)

V(t) = 18000(.12)^t ; $5013.02

12.

Growth or decay?

f(x) = 5/4 (.8)^x- 9

a)

Exponential Growth

b)

Exponential Decay

13.

Growth or decay?

f(x) = 4/5 (7/3)^x + 1

a)

Exponential Growth

b)

Exponential Decay

14.

Growth or decay?

f(x) = .25e^{x - 3} + 5

a)

Exponential Growth

b)

Exponential Decay

15.

Growth or decay?

f(x) = 3e^-x + 4

a)

Exponential Growth

b)

Exponential Decay

16.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

17.

Condense

a)

log₈(x⁶)/log₈(y³)

b)

log₈(x⁶/y³)

c)

log₈(x/y³)

d)

log₈(x⁶y³)

18.

Condense

a)

log₈x³y⁹

b)

log₈(x³/y⁹)

19.

Expand

a)

A

b)

B

c)

C

d)

D

20.

Evaluate

log₂(¹/₈) =

a)

-3

b)

3

c)

4

d)

-4

21.

Evaluate

10^log(k)=

a)

k

b)

10

c)

10^k

d)

1

22.

$\log_{25\ }5\ =$

a)

1

b)

25

c)

$\frac{1}{2}$

d)

5

23.

$\log_7\ 0=$

a)

Undefined

b)

0

c)

1

d)

$a$

24.

Evaluate

log(10^R)

a)

10

b)

1

c)

R

d)

10^R

25.

$\log_a\ 1\ =$

a)

Not defined

b)

0

c)

1

d)

$a$

26.

$\log_{\frac{1}{3}}\ 9$

a)

$\frac{1}{3}$

b)

2

c)

-2

27.

Evaluate

ln(e^W)

a)

e

b)

W

c)

e^W

d)

undefined

28.

Solve:
3^x-1 = 81

a)

5

b)

6

c)

9

d)

10

29.

Solve:
_{log (−2a + 9) = log (7 − 4a)}

a)

-5

b)

-1

c)

1

d)

5

30.

Solve: log₄x² = 1 + log₄(x-1)

a)

4

b)

3

c)

2

d)

1

31.

Solve:
lnx = 7.25

a)

1408.10

b)

1330.42

c)

1264.55

d)

1182.32

32.

Solve

log₂32 = 3x

a)

5/3

b)

3/5

c)

5

d)

3

33.

Solve

log₈₁x = 3/4

a)

2

b)

3

c)

27

d)

81

34.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

35.

Solve

a)

no solution

b)

6

c)

3

d)

2

36.

Solve

9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

37.

Solve

a)

-1/13

b)

1/11

c)

-2/11

d)

-2

38.

Solve

81^3-x = (1/3)^5x-6

a)

6

b)

-6

c)

9/2

d)

3/2

39.

Solve the equation.

$\log_{ }\left(3x+1\right)-\log\ \left(x\right)=\log_{ }\left(4\right)$

a)

x=16

b)

x=1

c)

x=0

d)

no solution

40.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

41.

log₅x - log₅(x+4)=log₅38

a)

-152/37, -8

b)

1/2

c)

-152/37

d)

No Solution

42.

Solve log₉ (x - 4) + log₉ (x + 1) = log₉ (x + 5) + log₉ (x - 6)

a)

17/2

b)

-9/16

c)

13

d)

-8

43.

Expand $\log_2\left(\frac{x}{3y}\right)$

a)

$\log_2\left(x\right)\ +\ \log_2\left(3\right)\ +\ \log_2\left(y\right)$

b)

$3\log_2\left(x\right)\ +\ \log_2\left(y\right)$

c)

$\log_2\left(x\right)\ -\ 3\log_2\left(y\right)$

d)

$\log_2\left(x\right)\ -\ \log_2\left(3\right)\ -\ \log_2\left(y\right)$

44.

-10log₂x + 8 = -12

a)

8

b)

12

c)

1296

d)

4

45.

$9\ +\ 10\log_8\ \left(-8x\right)\ =\ 19$

a)

$-\frac{5}{7}$

b)

$\frac{246}{49}$

c)

-1

d)

$-\frac{27}{4}$

46.

Solve. Round your answers to the nearest thousandth. $4\ln x=10$

a)

$x=2.5$

b)

$x=12.182$

c)

$x=11.992$

d)

$x=4.256$

47.

Solve for x:
5 ln (3x - 2) = 15

a)

x = 1.24

b)

x = 7.36

c)

x = 217,935.16

d)

x = 6.03

48.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

49.

Solve the equation. Round your answer to the nearest ten-thousandth. $-8\left(2^{n+5}\right)=-29.3$

a)

-4.4362

b)

No solution

c)

-3.1272

d)

=3.7019

50.

Solve the equation. Round your answer to the nearest ten-thousandth. $10\left(16^{v-3}\right)-3.3=28$

a)

4.141

b)

4.7752

c)

3.4115

d)

3.4955

51.

What is the asymptote value in the function?

a)

y = 3

b)

y = 2

c)

y = 7

d)

y = 0

Unit 4 Logs/Exps Test Review

Total questions: 51

Worksheet time: 4hrs 47mins

Similar Resources on Wayground