Logarithms: Definition, Properties, and Applications

Question 1

Which of the following is equivalent to log₁₀(1000)?

Accepted Answer

3

Answer

1/1000

Answer

-3

Answer

1/3

Question 2

If logₐ(b) = c, then which of the following is true?

Accepted Answer

a^c = b

Answer

a^b = c

Answer

c^a = b

Answer

b^c = a

Question 3

The Richter scale measures the magnitude of earthquakes using which scale?

Accepted Answer

Logarithmic

Answer

Linear

Answer

Quadratic

Answer

Exponential

Question 4

What is the domain of the function f(x) = log₁₀(x + 2)?

Accepted Answer

x > -2

Answer

x ≥ -2

Answer

x < -2

Answer

All real numbers

Question 5

Which of the following is a property of logarithms: logₐ(1) = ?

Accepted Answer

0

Answer

a

Answer

1

Answer

-1

Question 6

If the intensity of sound A is 100 times greater than the intensity of sound B, what is the difference in their decibel levels?

Accepted Answer

20 dB

Answer

10 dB

Answer

120 dB

Answer

100 dB

Question 7

The graph of y = log₂(x) is shifted 3 units to the left. What is the equation of the transformed graph?

Accepted Answer

y = log₂(x + 3)

Answer

y = log₂(x - 3)

Answer

y = log₂(x) - 3

Answer

y = log₂(x) + 3

Question 8

Which of the following is equivalent to log₃ 27?

Accepted Answer

3

Answer

1/3

Answer

9

Answer

27

Question 9

Which of the following logarithmic properties is **incorrect**?

Accepted Answer

logₐ (x + y) = logₐ x + logₐ y

Answer

logₐ (xy) = logₐ x + logₐ y

Answer

logₐ xⁿ = n logₐ x

Answer

logₐ (x/y) = logₐ x - logₐ y

Question 10

Solve for *x* in the equation: log₂ (x + 1) = 3

Accepted Answer

x = 7

Answer

x = 2

Answer

x = 1

Answer

x = 8

Question 11

Solve for *x* in the equation: log₃ (x²) - log₃ (x) = 2

Accepted Answer

x = 9

Answer

x = 3

Answer

x = -9

Answer

x = 1

Question 12

What is the value of log₂ 16?

Accepted Answer

4

Answer

8

Answer

1/2

Answer

2

Question 13

Which of the following expressions is equivalent to log₃ 27?

Accepted Answer

3

Answer

1/3

Answer

27

Answer

9

Question 14

If log₁₀ x = 2, what is the value of *x*?

Accepted Answer

100

Answer

10

Answer

5

Answer

20

Question 15

Which of the following statements is true about the graph of y = log₂ (x)?

Accepted Answer

The graph has a vertical asymptote at x = 0.

Answer

The graph is symmetrical about the y-axis.

Answer

The graph is a straight line.

Answer

The graph passes through the point (0, 1).

Question 16

Simplify the expression: log₄ 16 + log₄ 64

Accepted Answer

5

Answer

2

Answer

8

Question 17

Solve the equation log₃ (x + 2) = 2

Accepted Answer

x = 7

Answer

x = 9

Answer

x = 1

Answer

x = 4

Question 18

What is the value of log₅ √5?

Accepted Answer

1/2

Answer

1

Answer

5

Answer

2

Question 19

Which of the following logarithmic equations has a solution of x = 4?

Accepted Answer

log₂ (x - 2) = 1

Answer

log₅ (x - 3) = 1

Answer

log₄ x = 1

Answer

log₃ (x + 1) = 2

Question 20

The population of a city is growing exponentially. If the population doubles every 10 years, what is the annual growth rate (approximately)?

Accepted Answer

7%

Answer

5%

Answer

10%

Answer

2%