Free Printable QUIZ REVIEW Logarithms, properties & Solving

1.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

2.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

3.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

4.

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

5.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

6.

Write log₃ 81 = 4 in exponential form.

a)

81⁴=3

b)

81³=4

c)

4³=81

d)

3⁴=81

7.

Evaluate log₈ 8

a)

8

b)

-1

c)

0

d)

1

8.

Simplify log₄4^3x

^{(Hint: look closely this has a log base 4 AND and exponential base 4 both in the same problem)}

a)

3x

b)

3

c)

4

d)

4^3x

9.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

10.

Evaluate log₇ 343

a)

3

b)

49

c)

7

d)

1

11.

Evaluate. $\log_2\ \frac{1}{16}$

a)

4

b)

-4

c)

-2

d)

1/8

12.

Evaluate.

\log\ \frac{1}{100}

a)

–2

b)

1/2

c)

–1/2

d)

2

13.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

14.

Evaluate the following logarithm:

log₈√8

a)

-¹/₂

b)

-1

c)

1

d)

¹/₂

15.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

16.

evaluate log 10,000

a)

2

b)

3

c)

4

d)

10

17.

evaluate log₉ 3

a)

2

b)

-2

c)

1/2

d)

0

18.

evaluate log₉ 27

(Hint: try changing to "same base" and solving)

a)

2

b)

3/2

c)

2/3

d)

-3

19.

evaluate

\log_5\ \frac{1}{25}

a)

2

b)

-2

c)

5

d)

1/2

20.

lne

a)

0

b)

1

21.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

22.

Evaluate

\log_8\ \frac{1}{2}

a)

-3

b)

-1

c)

1/3

d)

-1/3

23.

Evaluate

\log_{16}\ 64

a)

1/2

b)

-2

c)

3/2

d)

2/3

24.

Evaluate

\log_{243}\ \frac{1}{27}

a)

-3/2

b)

-2/3

c)

-3/5

d)

-5/3

25.

Evaluate

\log_{16}\ 64

a)

2/3

b)

3/2

c)

3/5

d)

1/2

26.

Use the property Log_b(xy) = Log_b(x) + Log_b(y)

to expand: Log₃(5x)

a)

$\log_2\left(5\right)\ \times\ \log_2\left(x\right)$

b)

$\log_2\left(5\right)\ +\ \log_2\left(x\right)$

c)

$\log_2\left(5\right)\ -\ \log_2\left(x\right)$

d)

$\log_2\left(5\ +\ x\right)\$

27.

Use the property $\log_b\left(\frac{x}{y}\right)\ =\ \log_b\left(x\right)\ -\ \log_b\left(y\right)$ to expand $\log_2\left(\frac{x}{4}\right)\$

a)

$\log_2\left(x\right)\ \times\ \log_2\left(4\right)$

b)

$\log_2\left(x\right)\ +\ \log_2\left(4\right)$

c)

$\log_2\left(x\right)\ -\ \log_2\left(4\right)$

d)

$\log_2\left(5\right)\ -\ \log_2\left(x\right)\$

28.

Re-write using properties of logarithms: $\log_5100\ -\ 2\log_52$

a)

$\log_5\left(100\cdot4\right)=\log_5400$

b)

$\log_5\left(\frac{100}{2}\right)=\log_550$

c)

$\log_5\left(\frac{100}{2^2}\right)=2\log_550$

d)

$\log_5\left(\frac{100}{2^2}\right)=\log_525$

29.

When a logarithm has division inside of it, it expands using ________________.

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

30.

Use the property $\log_b\left(x\right)^a\ =\ a\log_b\left(x\right)\$
to expand $\log_5\left(x\right)^2\$

a)

$5\log_2\left(x\right)\$

b)

$2\log_5\left(x\right)\$

c)

$\log_5\left(x\right)\ +\ \log_5\left(2\right)$

d)

$\log_5\left(x\right)\ -\ \log_5\left(2\right)\$

31.

Use the properties of logs to condense the expression into a single log.

$\log\left(6\right)-\log\left(2\right)+\log\left(3x\right)$

a)

$\log\left(9x\right)$

b)

$\log\left(6x\right)$

c)

$\log\left(4x\right)$

d)

$\log\left(7x\right)$

32.

Expand $\log_2\left(\frac{x}{3y}\right)$

a)

$\log_2\left(x\right)\ +\ \log_2\left(3\right)\ +\ \log_2\left(y\right)$

b)

$3\log_2\left(x\right)\ +\ \log_2\left(y\right)$

c)

$\log_2\left(x\right)\ -\ 3\log_2\left(y\right)$

d)

$\log_2\left(x\right)\ -\ \log_2\left(3\right)\ -\ \log_2\left(y\right)$

33.

Use properties of Logs to write $\log_3\left(4\right)-\log_3\left(x\right)+\log_3\left(y\right)$

as one Log

a)

$\log_3\left(\frac{4x}{y}\right)\$

b)

$\log_3\left(4xy\right)$

c)

$\log_3\left(\frac{4}{xy}\right)$

d)

$\log_3\left(\frac{4y}{x}\right)$

34.

log₄(3x - 1) = log₄(2x + 3)

a)

4

b)

3

c)

1

d)

8

35.

log₆(2x + 16) = 3

a)

x = 2

b)

x = 100

c)

x = 116

d)

x = 50

36.

Solve the equation. $\log x-\log4\ =\ \log3$

a)

-1

b)

3/4

c)

7

d)

12

37.

Solve for x. $\log_52+\log_5x=\log_520$

a)

x = 20

b)

x = 10

c)

x = 2

d)

$x=\frac{1}{10}$

38.

Solve for x. $\log_4\left(x+3\right)+\log_42=4$

a)

x = 29

b)

x = 51

c)

x = 4

d)

x = 125

39.

Solve $\ln\left(3x-5\right)=6$ Which 2 choices are correct?

a)

136.143

b)

129.674

c)

$\frac{e^6-3}{5}$

d)

$\frac{e^6+5}{3}$

40.

$\log2+\log\left(x^2-3\right)=\log\ 282$

a)

12

b)

12, -12

c)

3, -3

d)

11, -11

41.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

42.

Solve for x, as a simplified fraction:

a)

x = 6 / 5

b)

x = 25 / 6

c)

x = 6 / 25

d)

x = 5 / 6

43.

Solve for x: $\log\left(x+9\right)+\log x=\log22$

Be sure to check all possible answers. Recall: you can NOT take log of "0" or a negative

a)

2, -11

b)

2

c)

-11

d)

11

44.

Converting forms: Convert the given exponential equation into its logarithmic form.

$3^x=y$

a)

$\log_3x=y$

b)

$\log_3y=x$

c)

$\log_xy=3$

d)

$\log_yx=3$

45.

Solving Log Equations: $-8\ \log_3\left(x+3\right)=-24$

a)

5

b)

13

c)

84

d)

24

QUIZ REVIEW Logarithms, properties & Solving

Total questions: 45

Worksheet time: 2hrs 44mins

Similar Resources on Wayground