# Definition and Properties of Logarithms

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Logarithms Learning Material
Tutorial IDTitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
13.1Definition and Properties of Logarithms

## Definition and Properties of Logarithms Revision Questions

1. . Which of the following is equivalent to 35 = 243?

1. log3 5 = 243
2. log5 3 = 243
3. log3 243 = 5
4. log5 243 = 3

2. . The expression log 62 is equivalent to

1. 6 log 2
2. 2 log 6
3. 2 log 10
4. log6 36

3. . The number 32 in the expression log2 32 = 5 represents the

1. Base
2. Argument
3. Logarithm
4. Exponent

4. . The expression log16 4 is equal to

1. 2
2. 4
3. 64
4. 1/2

5. . What is the result of the operation 4 log2 8 + log3 9?

1. 5
2. 9
3. 12
4. 14

6. . What is the result of the operations

log2 16 ∙ log4 64
1. 12
2. 24
3. 80
4. 1024

7. . What is the result of the operation

log4 80 - log4 5
1. 2
2. 75/4
3. 16
4. 100

8. . What is the value of the expression

log4 8 - log8 4
1. 5/6
2. 6/5
3. 1/2
4. -1/2

9. . The expression

2 log4 16/log7 49 - log 10
1. 2
2. 1
3. 0
4. -8

10. . Which of the following options is equivalent to

log35x7
1. 1/2 log3 5 + 7 log3 x
2. 1/2 (log3 5 + 7 log3 x )
3. 7 log3 5x
4. 7/2 log3 5x

11. . Which of the following options is equivalent to

40 log3 a - (8 log3 b + 16 log3 c)
1. log3 40a/148bc
2. log3 (40a - 8b - 16c)
3. log3 a40/b8 c16
4. 48 log3 a/bc

12. . What is the value of the expression

log1/4 32 + 5 log3 (1/3)2
1. 41/4
2. 15/2
3. -25/2
4. -15/2

13. . What is the value of the expression

log3 1/3 + log2 1/2 - 2 log5 1/5
1. -4
2. -2
3. 0
4. 4

14. . What is

log 1 + 3 log5 25
1. 4
2. 6
3. 7
4. 26

15. . What is

log 1/100 + log 1/10 - log 1 + log 10 - log 100
1. -1
2. 0
3. 1
4. 2

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

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