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The following math revision questions are provided in support of the math tutorial on Definition and Properties of Logarithms. In addition to this tutorial, we also provide revision notes, a video tutorial, revision questions on this page (which allow you to check your understanding of the topic) and calculators which provide full, step by step calculations for each of the formula in the Definition and Properties of Logarithms tutorials. The Definition and Properties of Logarithms calculators are particularly useful for ensuring your step-by-step calculations are correct as well as ensuring your final result is accurate.

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Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions |
---|---|---|---|---|---|

13.1 | Definition and Properties of Logarithms |

**1.** . Which of the following is equivalent to 3^{5} = 243?

- log
_{3}5 = 243 - log
_{5}3 = 243 - log
_{3}243 = 5 - log
_{5}243 = 3

**Correct Answer: C**

**2.** . The expression log 6^{2} is equivalent to

- 6 log 2
- 2 log 6
- 2 log 10
- log
_{6}36

**Correct Answer: B**

**3.** . The number 32 in the expression log_{2} 32 = 5 represents the

- Base
- Argument
- Logarithm
- Exponent

**Correct Answer: B**

**4.** . The expression log_{16} 4 is equal to

- 2
- 4
- 64
*1**/**2*

**Correct Answer: D**

**5.** . What is the result of the operation 4 log_{2} 8 + log_{3} 9?

- 5
- 9
- 12
- 14

**Correct Answer: D**

**6.** . What is the result of the operations

log_{2} 16 ∙ log_{4} 64

- 12
- 24
- 80
- 1024

**Correct Answer: A**

**7.** . What is the result of the operation

log_{4} 80 - log_{4} 5

- 2
- 75/4
- 16
- 100

**Correct Answer: A**

**8.** . What is the value of the expression

log_{4} 8 - log_{8} 4

*5**/**6**6**/**5**1**/**2**-1**/**2*

**Correct Answer: A**

**9.** . The expression

- 2
- 1
- 0
- -8

**Correct Answer: B**

**10.** . Which of the following options is equivalent to

log_{3} √**5x**^{7}

log*1**/**2*_{3}5 + 7 log_{3}x(log*1**/**2*_{3}5 + 7 log_{3}x )- 7 log
_{3}5x log*7**/**2*_{3}5x

**Correct Answer: B**

**11.** . Which of the following options is equivalent to

40 log_{3} a - (8 log_{3} b + 16 log_{3} c)

- log
_{3}*40a**/**148bc* - log
_{3}(40a - 8b - 16c) - log
_{3}*a*^{40}*/**b*^{8}c^{1}6 - 48 log
_{3}*a**/**bc*

**Correct Answer: C**

**12.** . What is the value of the expression

log_{1/4} 32 + 5 log_{3} (*1**/**3*)^{2}

*41**/**4**15**/**2**-25**/**2**-15**/**2*

**Correct Answer: C**

**13.** . What is the value of the expression

log_{3} *1**/**3* + log_{2} *1**/**2* - 2 log_{5} *1**/**5*

- -4
- -2
- 0
- 4

**Correct Answer: C**

**14.** . What is

log 1 + 3 log_{5} 25

- 4
- 6
- 7
- 26

**Correct Answer: B**

**15.** . What is

log *1**/**100* + log *1**/**10* - log 1 + log 10 - log 100

- -1
- 0
- 1
- 2

**Correct Answer: B**

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- Continuing learning logarithms - read our next math tutorial: Exponential and Logarithmic Equations

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