Ch. 7 Quiz Review (7.1-7.4) Name:_______________________________________________________________________________________Period:______ 1) Condense each expression using the properties of logarithms 1

a) log(4) + log(5)

b) log(5) − log(𝑥)

c) 5 log(𝑚) − 3log(𝑛)

d) 2 log(8) + log(𝑥) − log(10)

2

2) Expand each expression using the properties of logarithms 𝑥2

a) log(10𝑥)

b)

log (

c) log 4 𝑥 2 𝑦 3

d)

log (

100

)

𝑚2 𝑛 4

)

3) Use the change of base formula to evaluate each logarithm on the calculator. Round to 3 decimal places. a) log 3 5

b)

log 4 12

4) Write each equation in exponential form a) log 3 27 = 3

1

b) log 2 32 = 5

c) log 2 ( ) = −3 8

5) Write each equation in logarithmic form a) 62 = 36

b) 24 = 16

c) 641/2 = 8

6) Evaluate each logarithm without using a calculator. log 3 9

log 2 (8)

log 100

log 4 (

7) Evaluate each logarithm without using a calculator. Show your work. log 4 8

log 27 9

log16 32

1 ) 16

8) Write an exponential function for each situation. Then find the value of each function after 5 years. a)

A baseball card bought for $50 increases in 3% in value each year.

b)

A $12,500 car depreciates 9% each year.

9) Write an exponential for each table a)

x y

0 10

1 20

2 40

b)

3 80

x y

0 270

1 90

2 30

3 10

10) Complete the table below Equation

Starting Value

Growth or Decay?

increase Percent { decrease

Growth/Decay Factor

Y = 2(1.4)x Y = 3(0.25)x Y = 1.01x Y = 15(0.8)x

11) Graph the following functions. Describe the domain, range, and write the equation for the asymptote. 𝑦 = 3𝑥

𝑦 = log 3 𝑥

Domain:

-8

-6

-4

10

8

8

6

6

4

4

2

2

-2

2

4

6

8

10

X

-10

10

-10

-8

-6

-4

-4

-4

-6

-6

-8

-8

-10

-10

Asymptote:

𝑦 = 3𝑥−1 − 2

Domain:

Range:

4

6

8

Asymptote:

𝑦 = log 3 (𝑥 + 5) + 4

-6

-4

10

8

8

6

6

4

4

2

2

-2

Range:

2

4

6

8

10

X

-8

10

-10

-8

-6

-4

-2

2

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10

Asymptote:

Domain:

Range:

4

6

8

10

X

Y

Y

Domain:

2 -2

Range:

-10

-2

-2

Asymptote:

10

X

Y

Y