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Exponentials and Logarithms Review

Total questions: 40

Worksheet time: 2hrs 0mins

Name
Class
Date
1.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
2.
You invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years.
a)
$800.26
b)
$6,701.28
c)
$10,138.07
d)
$1,923.23
3.
Solve 8 = 25x+7
a)
⅘
b)
¼
c)
-⅘
d)
-¼
4.
Solve 33 = 34x + 2
a)
¼
b)
-¼
c)
½
d)
-½
5.
Solve for n:
2-2n = 26
a)
-1
b)
-7
c)
5
d)
-3
6.
Solve for b:
43b - 3 = 1/16
a)
7
b)
-1/4
c)
1/2
d)
1/3
7.
Solve for r:
3-3r = 35
a)
-4
b)
-5/3
c)
2
d)
8
8.
Solve for x:
32x = 27
a)
3/2
b)
-2
c)
0
d)
5
9.
Rewrite in exponential form:
log (x) = ¼
a)
x1/4 = 1
b)
1x =¼
c)
101/4 = x
d)
10x = ¼
10.
Evaluate.
log381
a)
4
b)
1/4
c)
-4
d)
-1/4
11.

Solve for x: log232=3x

a)

5/3

b)

3/5

c)

5

d)

3

12.

Solve for x: logx1000=3

a)

1

b)

10

c)

30

d)

3

13.
Write the following equation in exponential form:
log232 = 5
a)
25 = 32
b)
232 = 5
c)
52 = 32
d)
322 = 5
14.
Change to Exponential Form:
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
15.

Evaluate the following logarithm:


log327

a)

3

b)

2

c)

-3

d)

1/3

16.
Solve for x:
logx 25 = 2
a)
5
b)
-5
c)
1/5
d)
-1/5
17.
Solve for r:
3-3r = 35
a)
-4
b)
-5/3
c)
2
d)
8
18.

Solve for n: 7n+10- 8 = 6

a)

-7.374

b)

-8.643

c)

-7.360

d)

-8.853

19.
Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?
a)
$1,584.62
b)
$2,651.39
c)
$2,706.86
d)
$1,825.10
20.
Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.
a)
$15,415.94
b)
$15,683.28
c)
$15,927.56
d)
$16,109.05
21.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
22.
Approximately what interest rate would be needed in order to grow an investment of $1,400 to $2,500 in 10 years if the interest was compound monthly?
a)
5.96%
b)
5.84%
c)
5.81%
d)
5.88%
23.

In the compound interest formula A=P(1+r)t what does the A stand for?

a)

The amount of interest

b)

The total amount

c)

The interest rate

d)

The time

24.

In the compound interest formula A=P(1+r)t what does the P stand for?

a)

The time

b)

The total amount

c)

The principal amount (original amount)

d)

The interest rate

25.

Jacob borrows $500 from Abraham and agrees to have the loan compounded annually for 5 years with an interest rate of 2.5%. How much will the total amount be that Jacob owes?

a)

$565.70

b)

$262609.38

c)

$65.70

d)

$630.20

26.

Henry deposits $750 into a college savings account that is compounded annually when his parents received as a stimulus package. If Henry lets the money sit in the account without adding or removing any and receives a 8.5% interest rate, how much money will he have total after 5 years?

a)

$1127.74

b)

$1535.24

c)

$2345.67

d)

$850.76

27.

Trevor wants to have $4000 saved up in 3 years for a car. If he invests $1500 in a savings account that is compounded annually at an interest rate of 12%, will he have enough money at the end of the 4 years?

a)

Yes

b)

No

28.

What is the base of Log(45)?

a)

10

b)

45

c)

x

d)

1

29.

What is the base of log⁡3(x+9)=5\log_3\left(x+9\right)=5  

a)

3

b)

(x+9)

c)

x

d)

5

30.

Solve: log⁡3x=5\log_3x=5  

a)

x = 15

b)

x = 243

c)

x = 81

d)

x = 1235

31.

log⁡3(3x−11) = log⁡3(25−x)\log_3\left(3x-11\right)\ =\ \log_3\left(25-x\right)  

(a)  

32.

log⁡275=log⁡23+log⁡2(2y−1)\log_275=\log_23+\log_2\left(2y-1\right)  

(a)  

33.

log⁡(w2+21)=log⁡(10w)\log\left(w^2+21\right)=\log\left(10w\right)  

For 2 solutions put the lowest solution first, then comma and next number, no space.

(a)  

34.
Change 6.75% to a decimal.
a)
67.5
b)
.675
c)
675
d)
.0675
35.
Expand.
a)
log x + 5 log y
b)
5 log x + 5 log y
c)
5 log x - log y
d)
log x - 5 log y
36.
Solve
a)
5
b)
13
c)
84
d)
-20
37.

Match the word to the correct value of n.

a)

annually

1.

n = 1

b)

quarterly

2.

n = 4

c)

monthly

3.

n = 12

d)

weekly

4.

n = 52

e)

semi-annually

5.

n = 2

38.
Solve for x:  log6x + log6(x-5) = 2
a)
√7
b)
9
c)
4
d)
none of these
39.

Why should you avoid giving your personal information over the phone if you didn't initiate the call?

a)

To protect yourself from getting too much aid

b)

To protect yourself from identity theft

c)

To ensure the public can access your information

d)

You actually can give your information over the phone without any concerns.

40.

When squirrels feel threatened, they will run in a ________ way?

a)

Straight way

b)

Spiral way

c)

Zig-Zag way

d)

Triangle way

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