Free Printable Unit 13 Logarithms Review

1.

A collectible car is valued at $54,000 in 2020, the year it was made. It goes up in value at 9.5% annually. How much will it be worth in 2050?

a)

82,189.69

b)

821,896.89

c)

5,047,771.8

2.

If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.

a)

1.25mg

b)

1.25g

c)

10g

d)

10mg

3.

The half-life of strontium-90 is 25 years. How much strontium-90 will remain after 100 years if the initial amount is 4.0 g?

a)

3.0g

b)

0.25mg

c)

0.3g

d)

0.25g

4.

You have 100 grams of radioactive C-14. The half life of C-14 is 5730 years.
How many grams are left after 1 half life?

a)

100 grams

b)

25 grams

c)

2 grams

d)

50 grams

5.

Caiden earned $475 from mowing lawns last summer.He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

a)

$827.52 (Mr. Williams)

b)

$831.10 (Mrs. Hoch)

c)

$839.45 (Mr. Krajunus)

d)

$846.80 (Ms. Palombo)

6.

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

a)

$33,299.42 playing dodgeball

b)

$33,672.68 climbing trees

c)

$34,157.04 riding unicycles

d)

$34,710.88 flipping pancakes

7.

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much interest will she earn in 10 years?

a)

$915.59 Rome

b)

$933.28 Sydney

c)

$979.81 Dublin

d)

$1,005.09 Paris

8.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

9.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 year?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

10.

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

11.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

12.

Dash puts $4125 into an account using compounded continuously. If he keeps the money in the account for 5 years and now has a total of $4193.89. What is the interest rate?

a)

0.33%

b)

0.25%

c)

0.53%

d)

0.52%

13.

Chelsea put $7500 into an account paying 5% compounded continuously. She now has $10,643.01. How long has the money been in the account?

a)

7 years

b)

6 years

c)

5 years

d)

4 years

14.

How long will it take $3000 to double if it is invested in an account that pays 3% compounded continuously?

a)

23.1 years

b)

22.1 years

c)

21.1 years

d)

20.1 years

15.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

16.

Expand ln xy²z³

a)

6(lnx + lny - lnz)

b)

lnx + 2lny - 3lnz

c)

lnx + (1/2)lny + (1/3)lnz

d)

lnx + 2lny + 3lnz

17.

Solve the following equation for x. Round your solution to two decimal places.
ln2x - ln41 = 2

a)

x = 0.36

b)

x = 151.48

c)

x = 41

d)

None of these are solutions

18.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

19.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

20.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

21.

Which of the following is the value of x given;
e^(x + 6) = 12

a)

x = ln 6

b)

x = -6 + ln12

c)

x = ln72

d)

x = ln(-2)

22.

Which of the following is the value of x given;
7e^(3x-5) = 49

a)

x = 2.315

b)

x = 0.681

c)

x = 2.964

d)

No Solution

23.

Solve ln e

a)

10

b)

1

c)

5

d)

3

24.

Solve ln 1

a)

10

b)

4

c)

0

d)

1

25.

Expand ln(4x)

a)

ln4 + lnx

b)

ln 4 - lnx

c)

ln4x

d)

ln 4 - x

26.

Using a calculator approximate ln 2.3 to the nearest thousandth

a)

.832

b)

.833

c)

.834

d)

.924

27.

Using a calculator approximate ln 4.5 to the nearest ten thousandth

a)

1.5041

b)

1.5

c)

1.5040

d)

1.540

28.

condense 4ln7 + 2lnx

a)

ln7⁴x

b)

ln7x

c)

ln7x²

d)

ln7⁴x²

29.

Write the equation in logarithmic form.
$e^{\left(x-9\right)}=74$

a)

$\ln\left(x-9\right)=74$

b)

$x-9=\ln74$

30.

Expand the logarithmic expression.

$\ln\sqrt{r^8s^5}$

a)

$\ln r^4s^{\frac{5}{2}}$

b)

$\ln r^8+\ln s^{\frac{5}{2}}$

c)

$4\cdot\ln r+\frac{5}{2}\ln s$

d)

$4\cdot\ln r-\frac{5}{2}\ln s$

31.

Solve the equation. Round your answer to four decimal places.
$3e^x+1=5$
$x=$ (a)

32.

Evaluate:
$\ln e^{28}=x$

a)

$2.718$

b)

$14$

c)

$26$

d)

$28$

33.

Evaluate:
$\ln3=x$

a)

$0.405$

b)

$1.099$

c)

$1.504$

d)

$1.792$

34.

Solve for x.

a)

3

b)

16

c)

10

d)

8

35.

Solve the equation:

log₁₁b = 3

a)

1331

b)

16

c)

1000

d)

$\frac{1}{9}$

36.

$\log_9\left(r-8\right)\ =\ 2$

a)

55

b)

$\frac{11}{6}$

c)

89

d)

6

37.

Solve the equation:

$5^{\left(2-3x\right)}=25$

a)

$\frac{7}{5}$

b)

$-\frac{3}{4}$

c)

$-\frac{7}{6}$

d)

$0$

38.

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

39.

Solve for x

e^{\left(3x-1\right)}=2

a)

0.564

b)

0

c)

0.693

d)

1.079

40.

Solve for x

e^{\left(x+1\right)}=6

a)

1.609

b)

0.792

c)

1.792

d)

1096

41.

ln (5x + 6) = 5

a)

154.413

b)

30.883

c)

147.213

d)

28.483

42.

Solve the following equation. Round to the nearest ten-thousandth. (Challenge Question!)

$\ln\left(x\right)-\ln\left(x-1\right)=5$

a)

4.2587

b)

1.0068

c)

2.6879

d)

0.2879

43.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

44.

Use the change of base formula and your calculator to approximate the log.

a)

A

b)

B

c)

C

d)

D

45.

Evaluate.

log₆(¹/₂₁₆) = x

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

46.

Logarithms are the inverse of ___________.

a)

Linear

b)

Quadratics

c)

Cubes

d)

Exponential

47.

Expand log₅(u³v⁵)

a)

1/2(log₅u+log₅v+log₅uw)

b)

5 log₅u - 15 log₅ v

c)

log₅u + log₅v +3 log₅w

d)

3 log₅u + 5 log₅v

48.

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)

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

49.

Use the change of base rule to rewrite this problem:

log₃36

a)

$\frac{\log36}{\log3}$

b)

$\frac{\log\ 3}{\log\ 36}$

c)

log 12

d)

$\log\ \frac{1}{12}$

50.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

51.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

52.

Write as a Single Log

$\ln\left(3\right)+2\ln\left(5\right)-7$

a)

$\ln75e$

b)

$\ln\left(\frac{75}{e^7}\right)$

c)

$\ln\left(\frac{75}{7}\right)$

d)

$\ln\left(30\right)-7$

53.

Write in terms of $\log_4y$ and $\log_4x$

$\log_4\sqrt[2]{x^3}y^5$

a)

$2\log_4x+\log_4\sqrt[2]{y^3}$

b)

$\frac{2}{3}\log_4x+5\log_4y$

c)

$\frac{3}{2}\log_4x-5\log_4y$

d)

$\frac{3}{2}\log_4x+5\log_4y$

54.

Quarterly means how many times a year?

a)

4

b)

2

c)

1

d)

6

Unit 13 Logarithms Review

Total questions: 54

Worksheet time: 14hrs 30mins

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