Quiz about Exponential and Logarithmic Review

Question 1

Evaluate b^log_b(x)

Accepted Answer

x

Answer

b

Answer

1

Answer

0

Question 2

Evaluate log_b(1)

Accepted Answer

0

Answer

1

Answer

-1

Answer

b

Question 3

Evaluate log_b(b)

Accepted Answer

1

Answer

-1

Answer

0

Answer

b

Question 4

Evaluate log_b(b^x)

Accepted Answer

x

Answer

1

Answer

0

Answer

b

Question 5

Expand log₆(5x³/y).

Accepted Answer

log₆5+3log₆x-log₆y

Answer

log₆5x³-log₆y

Answer

log₆5+log₆x³-log₆y

Question 6

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

Accepted Answer

log 98

Answer

log 78

Answer

log 56

Answer

log 45

Question 7

How much of a radioactive kind of gallium will be left after 6 days if the rate of decay is 1/2 every 3 days and you start with 56 grams?

Accepted Answer

14 grams

Answer

.875 grams

Answer

126 grams

Answer

638 grams

Question 8

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

Accepted Answer

Exponential Growth

Answer

Exponential Decay

Answer

Linear

Answer

None of the above

Question 9

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

Accepted Answer

y = 15(1.35)^x

Answer

y = 15(35)^x

Answer

y = 15(0.35)^x

Answer

y = 35(1.15)^x

Question 10

Simplify:
(3t²)³

Accepted Answer

27t6

Answer

9t6

Answer

9t5

Answer

27t5

Question 11

Using change of base solve log₇8=?

Accepted Answer

1.069

Answer

.936

Answer

.903

Answer

1.892

Question 12

7x=17

Accepted Answer

x=1.456

Answer

x=.687

Answer

x=1.546

Answer

x=.786

Question 13

Evaluate using change of base.
log₆(¹/₂₁₆)

Accepted Answer

-3

Answer

3

Answer

1/3

Answer

-1/3

Question 14

If a savings fund pays interest at a rate of 6% per year compounded continuously, how much money will you have if you invest $4000 after 4 years?

Accepted Answer

$5080

Answer

$3020

Answer

$3160

Answer

$1080

Question 15

log₂(x + 5) = 3

Accepted Answer

3

Answer

4

Answer

5

Answer

6

Question 16

4^(x-2)= 64

Accepted Answer

5

Answer

-2

Answer

-5

Answer

2

Question 17

(5³x²y⁴)⁰

Accepted Answer

1

Answer

5xy

Answer

0

Answer

5

Question 18

(y9)-2

Accepted Answer

1/y18

Answer

y18

Answer

y11

Answer

y9/2

Question 19

Solve

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 20

Solve

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 21

Solve

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 22

Solve

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 23

What kind of shift happens with this function?

Accepted Answer

4 points down

Answer

4 points up

Answer

4 points to the left

Answer

4 points to the right

Question 24

What kind of shift  is represented?

Accepted Answer

right 1 unit

Answer

up 1 unit

Answer

left 1 unit

Answer

down 1 unit

Question 25

Identify the y-intercept and whether the function is growth or decay.

Accepted Answer

4; decay

Answer

4; growth

Answer

1/2; growth

Answer

1/2; decay

Question 26

What transformations occur in the following function?

Accepted Answer

right 3, up 2

Answer

left 3, up 2

Answer

left 3, down 2

Answer

right 3, down 2

Question 27

If the number of bacteria in a colony doubles every 16 hours and there is currently a population of 3,000 bacteria, what will the population be 32 hours from now?

Accepted Answer

12,000 Bacteria

Answer

1.2 x 10¹³ Bacteria

Answer

196,608,000 Bacteria

Answer

6000 Bacteria

Question 28

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

Accepted Answer

f(x)=400(1+0.03)^x

Answer

f(x)=400(1+3)^x

Answer

f(x)=400(1-0.03)^x

Answer

f(x)=400(0.03)^x

Question 29

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

Accepted Answer

y=15,000(0.92)^x

Answer

y=8(15,000)^x

Answer

y=15,000(1.08)^x

Answer

y=15,000(0.08)^x

Question 30

Solve

Accepted Answer

1000

Answer

10

Answer

30

Answer

3

Question 31

Solve

Accepted Answer

2.389

Answer

1.414

Answer

0.182

Answer

-4.865

Question 32

Question 32.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 33

Given y=3^xdetermine the y-intercept and whether the function represents a growth or decay model.

Accepted Answer

(0,1); growth

Answer

(0,3); growth

Answer

(0,1); decay

Answer

(0,3); decay

Question 34

Identify the y-intercept

Accepted Answer

(0, 5)

Answer

(5, 0)

Answer

(1.2, 0)

Answer

(0, 1.2)

Question 35

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

Accepted Answer

y=5000(0.7)^x

Answer

y=30(5000)^x

Answer

y=5000(1.3)^x

Answer

y=5000xx

Question 36

Identify the asymptote of the function.

Accepted Answer

y = 2

Answer

y = -2

Answer

x = 2

Answer

y = 0

Question 37

Rewrite log₂8 = 3 in exponential form.

Accepted Answer

23 = 8

Answer

28 = 3

Answer

32 = 8

Answer

83 = 2

Question 38

Condense

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 39

Expand

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 40

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

Accepted Answer

Exponential Decay

Answer

Exponential Growth

Answer

Linear

Answer

Logarithmic

Question 41

The common logarithm has what base?

Accepted Answer

10

Answer

0

Answer

e

Answer

-e

Question 42

Graph

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 43

Graph

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 44

How are exponentials and logarithms related?

Accepted Answer

They're inverses

Answer

They're cousins

Answer

They're not related

Answer

They're reciprocals

Question 45

Which has the point (1,0) in the parent function?

Accepted Answer

logarithm

Answer

exponential

Answer

both

Question 46

Which has the point (0,1) in the parent function?

Accepted Answer

exponential

Answer

logarithm

Answer

both

Question 47

The natural logarithm is represented as what?

Accepted Answer

ln

Answer

log

Answer

ex

Answer

bx

Question 48

The natural logarithm has what base?

Accepted Answer

e

Answer

10

Answer

0

Answer

-e

Question 49

What is the vertical asymptote of
y = log₃(x) +2 ?

Accepted Answer

x = 0

Answer

x = 2

Answer

x = -2

Answer

y = 2

Question 50

What is the log form of a = e^y ?

Accepted Answer

ln(a) = y

Answer

ln(y) = a

Answer

log(a) = y

Answer

log(y) = a

Question 51

Change to Exponential Form:
log₆36 = 2

Accepted Answer

62=36

Answer

26=36

Answer

362=6

Answer

366=2

Question 52

Write the exponential equation as a logarithm
6³=216

Accepted Answer

log₆(216)=3

Answer

log₆(3) = 216

Answer

log₃(6) = 216

Answer

log₂₁₆(6)=3

Exponential and Logarithmic Review

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