Quiz about QUIZ REVIEW Logarithms, properties & Solving

Question 1

Logarithmic functions are the inverse of...

Accepted Answer

Exponential Functions

Answer

Linear Functions

Answer

Quadratic Functions

Answer

Polynomial Functions

Question 2

Rewrite 3⁴ = 81 in logarithmic form.

Accepted Answer

log₃81 = 4

Answer

log₃4 = 81

Answer

log₈₁3 = 4

Answer

log₄81 = 3

Question 3

The common logarithm has what base?

Accepted Answer

10

Answer

0

Answer

e

Answer

-e

Question 4

Rewrite log₂8 = 3 in exponential form.

Accepted Answer

23 = 8

Answer

28 = 3

Answer

32 = 8

Answer

83 = 2

Question 5

Write log₃ 81 = 4 in exponential form.

Accepted Answer

34=81

Answer

814=3

Answer

813=4

Answer

43=81

Question 6

Evaluate log₈ 8

Accepted Answer

1

Answer

8

Answer

-1

Answer

0

Question 7

Simplify log₄4^3x

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

Accepted Answer

3x

Answer

3

Answer

4

Answer

43x

Question 8

log₅25 = ?

Accepted Answer

2

Answer

5

Answer

125

Answer

10

Question 9

Evaluate log₇ 343

Accepted Answer

3

Answer

49

Answer

7

Answer

1

Question 10

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

Accepted Answer

-4

Answer

4

Answer

-2

Answer

1/8

Question 11

Evaluate log₄1

Accepted Answer

0

Answer

1

Answer

4

Answer

undefined

Question 12

Solve for x:
log₄ x = 3

Accepted Answer

64

Answer

4

Answer

12

Answer

32

Question 13

evaluate log 10,000

Accepted Answer

4

Answer

2

Answer

3

Answer

10

Question 14

evaluate log₉ 3

Accepted Answer

1/2

Answer

2

Answer

-2

Answer

0

Question 15

evaluate log₉ 27

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

Accepted Answer

3/2

Answer

2

Answer

2/3

Answer

-3

Question 16

lne

Accepted Answer

1

Answer

0

Question 17

The natural logarithm has what base?

Accepted Answer

e

Answer

10

Answer

0

Answer

-e

Question 18

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

to expand: Log₃(5x)

Accepted Answer

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

Answer

$$\log_2\left(5 ight)\ imes\ \log_2\left(x ight)$$

Answer

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

Answer

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

Question 19

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

Accepted Answer

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

Answer

$$\log_2\left(x ight)\ imes\ \log_2\left(4 ight)$$

Answer

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

Answer

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

Question 20

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 21

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

Accepted Answer

Subtraction

Answer

Addition

Answer

Multiplication

Answer

Division

Question 22

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

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

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 24

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 25

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

as one Log

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 26

log₄(3x - 1) = log₄(2x + 3)

Accepted Answer

4

Answer

3

Answer

1

Answer

8

Question 27

log₆(2x + 16) = 3

Accepted Answer

x = 100

Answer

x = 2

Answer

x = 116

Answer

x = 50

Question 28

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

Accepted Answer

12

Answer

-1

Answer

3/4

Answer

7

Question 29

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

Accepted Answer

x = 10

Answer

x = 20

Answer

x = 2

Answer

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

Question 30

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

Accepted Answer

x = 125

Answer

x = 29

Answer

x = 51

Answer

x = 4

Question 31

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

Accepted Answer

136.143

Accepted Answer

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

Answer

129.674

Answer

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

Question 32

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

Accepted Answer

12, -12

Answer

12

Answer

3, -3

Answer

11, -11

Question 33

log₄(3x-1)=log₄(2x+3)

Accepted Answer

4

Answer

3

Answer

1

Answer

8

Question 34

Solve for x, as a simplified fraction:

Accepted Answer

x = 5 / 6

Answer

x = 6 / 5

Answer

x = 25 / 6

Answer

x = 6 / 25

Question 35

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

Accepted Answer

2

Answer

2, -11

Answer

-11

Answer

11

Question 36

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

$$3^x=y$$

Accepted Answer

$$\log_3y=x$$

Answer

$$\log_3x=y$$

Answer

$$\log_xy=3$$

Answer

$$\log_yx=3$$

Question 37

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

Accepted Answer

24

Answer

5

Answer

13

Answer

84

QUIZ REVIEW Logarithms, properties & Solving

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