Free Printable Unit 3 Test Review - Exponential and Logarithmic Equations

1.

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

2.

What is the base in the equation

log x = 3?

a)

x

b)

10

c)

3

d)

1

e)

0

3.

When you have ONE logarithm in an equation, you must do what to solve the problem?

a)

Add another logarithm in.

b)

Make sure the base is 10.

c)

Convert to an exponential.

d)

Guess the answer.

4.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

5.

Expand the following logarithm:

log₃ (10z)

a)

log₃ 10 - log₃ z

b)

log₃ 10 + log₃ z

c)

zlog₃ 10

d)

log₃ z¹⁰

6.

Condense the following logarithm: lnx + ln4

a)

ln 4x

b)

ln 4/x

c)

log 4 + log x

d)

ln x⁴

7.

Rewrite in exponential form: $\log_{\left(x+y\right)}49=2$

a)

$\left(x+y\right)^2=49$

b)

$\left(x+y\right)^{49}=2$

c)

$49^2=\left(x+y\right)$

8.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

9.

Condense

a)

A

b)

B

c)

C

d)

D

10.

Condense

a)

A

b)

B

c)

C

d)

D

11.

Write in exponential form

a)

A

b)

B

c)

C

d)

D

12.

State the property(s) used to expand the expression

\log_4\left(\frac{20}{x^3}\right)\ =\ \log_420-3\log_4x

a)

Power Property

b)

Quotient Property

c)

Quotient and Power Property

d)

Product and Power Property

13.

State the property (s) used to simplify the expression

6log 2 = log 64

a)

Product Property

b)

Quotient Property

c)

Power Property

d)

Product and Power Property

14.

State the property(s) used to expand the expression

\log_3\left(a^2b^5\right)\ =\ 2\log_3a+5\log_3b

a)

Power Property

b)

Quotient Property

c)

Quotient and Power Property

d)

Product and Power Property

15.

Which equation will help you solve for x?
$\log_6\left(3x+2\right)=\log_6\left(5x-8\right)$

a)

$3x+2+5x-8=0$

b)

$6^{\left(5x-8\right)}=3x+2$

c)

$3x+2=5x-8$

d)

No equation will help you

16.

Which equation will help you solve for x?

\log_3\left(8\right)+\log_3\left(2x\right)=5

a)

$\frac{1}{4}x=5$

b)

$3^5=16x$

c)

$16x=5$

d)

$3^5=4x$

17.

Which equation will help you solve for x?
$\log\left(3x+25\right)=2$

a)

$3x+25=2$

b)

$2^2=3x+25$

c)

No equation will help you

d)

$10^2=3x+25$

18.

Which equation will help you solve for x?

\log_2\left(x-4\right)=6

a)

x - 4 = 6²

b)

6₂ = x - 4

c)

2^(x-4) = 6

d)

2⁶ = x - 4

19.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

20.

What is the equation for calculating pH?

a)

pH = [H⁺]

b)

pH = log [H⁺]

c)

pH = -log[OH^-]

d)

pH = -log [H⁺]

21.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

22.

Solve for x:

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

23.

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

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

24.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

25.

Solve the equation for x.

a)

x = 2

b)

x = 36

c)

x = 6

d)

x = 11

26.

To solve 8 = 2^5x+7, you would need to re-write 8 as what?

a)

$2^4$

b)

$4^2$

c)

$2^3$

27.

Use your calculator to solve. Round to four decimal places.

$\log_7\ 5$

a)

0.8271

b)

1.2091

c)

0.1461

d)

1.5441

28.

What is the pH of a solution with a hydrogen ion concentration of 6.2 x 10^-5?

a)

5

b)

4.2

c)

1.6

d)

10.9

29.

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

a)

5

b)

-5

c)

1/5

d)

-1/5

30.

The pH of a solution is 8.43. What is the [H⁺]concentration?

a)

3.7 x 10 ^-9

b)

1.0 x 10^-8.43

c)

2.7 x 10^-6

d)

1.0 x 10^-14

31.

$\left(x+9\right)^2=30$ Write the exponential equation as a logarithm

a)

$\log_{30}\left(x+9\right)=2$

b)

$\log_230=x+9$

c)

$\log_{\left(x+9\right)}30=2$

d)

$\log_{\left(x+9\right)}2=30$

32.

Solve for x:
$6^{3x}=1296$

a)

-1.6

b)

1.3

c)

1.1

d)

3.4

33.

The half-life of Strontium-90 is 25 years. How many years will it take for a sample to decay to 12.5 grams if the initial amount is 200 grams? $12.5=200\left(\frac{1}{2}\right)^{\frac{t}{25}}$

a)

125 years

b)

75 years

c)

50 years

d)

100 years

34.

Solve for x:
8^x+1= 3

a)

0.528

b)

0.893

c)

-0.472

d)

1.893

35.

Barium-122 has a half-life of 2 minutes. A fresh sample weighing 80 grams was obtained. How long will it take for the sample to decay and have 5 grams remaining?

a)

8 minutes

b)

10 minutes

c)

4 minutes

d)

12 minutes

36.

Expand the logarithm

a)

$\ln\left(x+1\right)+\ln\sqrt[4]{x-5}$

b)

$\ln\left(x+1\right)-\ln\sqrt[4]{x-5}$

c)

$\ln\left(x+1\right)-\frac{1}{4}\ln\left(x-5\right)$

37.

Expand the logarithm

a)

$2\log_{10}\left(a\right)+3\log_{10}\left(b\right)$

b)

$\frac{1}{2}\log_{10}\left(a\right)+\frac{1}{3}\log_{10}\left(b\right)$

c)

$\frac{1}{2}\log_{10}\left(a\right)-\frac{1}{3}\log_{10}\left(b\right)$

38.

Expand the logarithm.

a)

$\frac{1}{2}\log_z33-\frac{1}{2}\log_z19$

b)

$\log_z\sqrt[]{33}+\log_z\sqrt[]{19}$

c)

$\sqrt[]{\log_z33-\log_z19}$

39.

a)

x = 5 and x = -2

b)

x = -2

c)

x = 5

d)

x = -10 and x = 10

40.

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

a)

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

b)

$x-9=\ln74$

41.

Write the equation in exponential form.
$\ln53=x$

a)

$e^{53}=x$

b)

$e^x=53$

42.

Condense the expression as a single logarithm.

$\ln4+\ln3x$

a)

$\ln7x$

b)

$\ln\left(3x\right)^4$

c)

$\ln12x$

43.

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

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

44.

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

45.

Solve the equation. Round your answer to the nearest ten-thousandth. $8\left(16^{4.2n}\right)=72$

a)

0.1887

b)

0.5231

c)

0.4241

d)

0.2272

46.

A sample of fruit juice is found to have a hydrogen ion concentration of 2.87 x 10^-4. What would the pH be?

a)

1.76

b)

3.54

c)

8.29

d)

13.22

47.

The pH of a solution is 7.1. What is the [H₃O⁺]concentration?

a)

3.7 x 10 ^-9

b)

1.0 x 10^-7.1

c)

7.9 x 10^-8

d)

8.9 x 10^-7

48.

What is the pH of a solution when [H⁺] = 7.9 x 10^-11?

a)

2.4

b)

10.1

c)

7.5

d)

4.8

49.

The expression A(t) = 12(1.025)^t models the current population growth of elephants in a medium-sized wildlife refuge.
How many years will it take for the population to reach 25 elephants at the refuge ?

a)

20 years

b)

25 years

c)

30 years

d)

15 years

50.

If $1,000 is invested at 16% interest, compounded continuously, how long will it take for the investment to grow to $10,000? $A=P\cdot e^{\left(rt\right)}$

a)

About 12 years

b)

About 15 years

c)

About 18 years

d)

About 10 years

Unit 3 Test Review - Exponential and Logarithmic Equations

Total questions: 50

Worksheet time: 4hrs 10mins

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