Ch 10. Exponentials and Logarithms

Which of the following is an exponential function?

1. f(x) = 5x + 2

2. f(x) = 4x * 2^x

3. f(x) = 4x²

4. f(x) = 5 / x

5. f(x) = x³ + 2x² - 6

f(x) = 4x * 2x

Which equation represents a pattern that starts at 6 and is multiplied by 4 each step?

1. y = 6*(4²)

2. y = 24^x

3. y = 6*(4^x)

4. y = 4*(6²)

5. y = 4*(6^x)

y = 6*(4x)

In an exponential function, the exponent is which one of the following?

1. The variable

2. The decimal

3. The absolute value

4. The polynomial

5. The constant

The variable

A colony of bacteria starts with 9 bacteria at noon. If the number of bacteria triples every 20 minutes, how many bacteria will be present at 2:40 pm that afternoon?

1. 2,304

2. 589,824

3. 19,683

4. 59,049

5. 177,147

59,049

A value that a function will get infinitely close to, but never reach is called which one of the following?

1. An inequality

2. An equation

3. An asymptote

4. An exponential function

5. Exponential decay

An asymptote

In exponential growth, _____, while in exponential decay, _____.

1. the numbers get smaller; the numbers get bigger

2. the patterns of numbers are continuously divided; the patterns of numbers are continuously multiplied

3. the base of the exponential is greater than 1; the base of the exponential falls between 0 and 1

4. the base of the exponential falls between 0 and 1; the base of the exponential is greater than 1

the base of the exponential is greater than 1; the base of the exponential falls between 0 and 1

Which of the following equations represents an exponential decay?

1. y = (3/4)2^x

2. y = 2(3/4)^x

3. y = 4^x

4. y=3(2)^x

5. y = x² + 1

y = 2(3/4)x

Which of these equations correctly represents the following scenario: In her prime, 40 million people knew who Britney Spears was, but that number has decreased by 10% yearly. Since 90% of people still recognize her each year, what equation calculates how many people still know who Britney Spears is after a given number of years?

1. y = 0.1x + 40,000,000

2. y = 0.9(40,000,000)^x

3. y = 40,000,000(0.01)^x

4. y = 40,000,000(0.9)^x

5. y = 0.01(40,000,000)^x

y = 40,000,000(0.9)x

Every year a laptop is worth 1/3 of what it was worth for each year previous. If you have a $600 laptop, how much is it worth after 15 years?

1. $0.91

2. $400

3. $0.00004

4. $2.06

5. $1.37

$0.00004

A logarithm is the reverse or inverse of a/an _____ expression.

1. polynomial

2. functional

3. rational

4. exponential

exponential

Which of the following expressions are equivalent to each other?

1. A and B only

2. A and C only

3. A, B, and C

4. B and C only

A and C only

Which part of the logarithmic expression shown is the base?

1. log

2. c

3. b

4. a

a

What does x equal in the following equation:

1. x = 16

2. x = 3

3. x = 256

4. x = 60

x = 3

Use the following information to answer the question.

1. A

2. D

3. C

4. B

5. E

C

Evaluate the following.

1. 2

2. 216

3. -6

4. -2

5. 6

-2

Evaluate the following.

1. 1/3

2. 4

3. 16

4. 3

5. 2

3

Evaluate the logarithm below to 2 decimal places.

1. 2.29

2. 2.11

3. 1.48

4. 0.47

5. 0.70

2.11

Which expression is equivalent to log having base = e?

1. 

2. 

3. 

4. 

5. 

Evaluate the following.

1. 3

2. 1

3. 4

4. -2

5. 2

3

What does the quotient property of logarithms tell us to do?

1. Turn division on the inside into subtraction on the outside.

2. Turn division on the inside into multiplication on the outside.

3. Turn multiplication on the inside into addition on the outside.

4. Turn multiplication on the inside into subtraction on the outside.

Turn division on the inside into subtraction on the outside.

Which two log properties were used in this transformation?

1. quotient and power

2. power and product

3. change of base and power

4. quotient and product

power and product

What is this expression equal to?

1. 

2. 

3. 

4. 

Which property of logarithms is being applied in this image?

1. Quotient

2. Product

3. Power

4. Exponent

Power

Which property does this represent?

1. change of base

2. product

3. quotient

4. power

quotient

Condense the logarithm below:

1. 

2. 

3. 

4. 

5. 

Evaluate the logarithm below:

1. 10.00

2. 0

3. 1.00

4. 1.60

5. 1.25

1.00

Which logarithmic property is shown below?

1. Associative property

2. Power property

3. Distributive property

4. Quotient property

5. Product property

Product property

Evaluate the logarithm below:

1. 7

2. 8

3. 2.5

4. 5.5

5. 10

2.5

Expand the following logarithm:

1. 

2. 

3. 

4. 

5. 

Solve the following equation:

10^x + 9 = 11

1. 0.103

2. 0.402

3. 0.204

4. 0.301

0.301

Solve the following equation:

e^2x = 40

1. 2.312

2. 1.844

3. 0.768

4. 3.564

1.844

For which of the following problems will you use the natural log to help you solve it?

1. 10^x = 45

2. 4^x + 5 = 30

3. 3^3x + 2 = 9

4. e^{x + 2} = 40

e^x + 2 = 40

Solve the following equation:

10^{x - 3} = 10

1. 6

2. 5.456

3. 4

4. 1.32

4

Solve the following equation:

10^2x - 2 (10^x) + 1 = 0

1. 0.101 and 0.210

2. 1 and 2

3. 0 and 0

4. 0 and 0.101

0 and 0

What is the diameter (D) of the lens (in mm) that is required by a telescope to see stars of magnitude (M) = 17?

Use the logarithmic equation M = 5 log D + 2 where M is magnitude and D is diameter.

1. 15

2. 17

3. 10

4. 3

5. 1000

1000

When the log (of the same base) is the outermost step on both sides of the equation, the logs _____.

1. are multiplied

2. are subtracted

3. are added

4. cancel out

5. are divided

cancel out

The inverse operation of a log is a(an) _____.

1. radical

2. natural log

3. exponent

4. sine

5. tangent

exponent

Solve the following equation for x: 2 +2ln(x) = ln(x) + ln(2).

1. 

2. 

3. 

4. 

5. 

Solve for x in the equation log(3x) + log(5) = 1.

1. 1/5

2. 1/15

3. 3/5

4. 2/3

5. 5

2/3