Free Printable Unit 5 Review Math III

1.

Expand the following: $\log_5\left(z^8\right)$

a)

$5\log_8\left(z\right)$

b)

$8\log_5\left(z\right)$

c)

$\log_5\left(8z\right)$

d)

$8+\log_5\left(z\right)$

2.

Simplify the following: $\log_324-\log_36$

a)

$\log_318$

b)

$\log_3144$

c)

$\log_34$

d)

$\log12$

e)

$18\log3$

3.

Simplify the following: $\log_5\left(3\right)+\log_5\left(r\right)-\log_5\left(w\right)$

a)

$\log_5\left(3rw\right)$

b)

$\log_5\left(3+r-w\right)$

c)

$\log_5\left(\frac{3r}{w}\right)$

d)

$\frac{\log_5\left(3r\right)}{\log_5\left(w\right)}$

4.

Solve $\log_2\left(x+8\right)=\log_264$

a)

x=16

b)

x=24

c)

x=56

d)

x=40

5.

Example: Anne currently brings in an annual salary of $46,000 and anticipates a raise of 5% every year.

Is this problem describing exponential growth or decay?

a)

Growth

b)

Decay

6.

Example: Anne currently brings in an annual salary of $46,000 and anticipates a raise of 5% every year.

Convert the growth percentage to a decimal.

(a)

7.

Anne currently brings in an annual salary of $46,000 and anticipates a raise of 5% every year.

We now know that our r value is .05. What is our P value? (p is the starting value)

No dollar sign.

(a)

8.

Anne currently brings in an annual salary of $46,000 and anticipates a raise of 5% every year. What will her salary be in 4 years?

Using a calculator or Desmos, answer the question by plugging in 4 for x. Round your answer to the nearest dollar: $ (a)

9.

Example: A car bought for $13,000 depreciates at 12% annually.

Is this problem describing exponential growth or decay?

a)

Growth

b)

Decay

10.

Example: A car bought for $13,000 depreciates at 12% annually.

Convert the decay percentage to a decimal.

(a)

11.

A car bought for $13,000 depreciates at 12% annually.

We now know that our r value is .12. What is our P value? (P is the starting value)

(a)

12.

A car bought for $13,000 depreciates at 12% annually. What will the car be worth after 10 years?

Using a calculator or Desmos, answer the question by plugging in 10 for x. Round your answer to the nearest dollar: $ (a)

13.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

14.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

15.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

16.

Solve the equation for x

a)

1.585

b)

3.169

c)

0.792

d)

1.084

17.

Condense: $3\log_5\ a\ -\ 4\log_5\ b\ +5\ \log_5\ c$

18.

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

19.

Solve: $\log_x1024=5$

a)

4

b)

5

c)

8

d)

$\frac{1}{4}$

20.

Condense: log16 + log2 - log8

a)

log4

b)

log8

c)

log10

d)

log24

Unit 5 Review Math III

Total questions: 20

Worksheet time: 35mins

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