# Natural Logarithm Function and Its Graph

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Logarithms Learning Material
Tutorial IDTitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
13.4Natural Logarithm Function and Its Graph

## Natural Logarithm Function and Its Graph Revision Questions

1. . Which of the following options is false?

1. ln x2 = 2 ln x
2. ln (2x) = ln 2 + ln x
3. ln (3x) = loge (3x)
4. ln x5 = x5 ln e

2. . What is the value of ln (2e)2?

1. 2
2. 4
3. 2 + 2·ln 2
4. 4 ln e

3. . What is

2 ln x - 3 ln x2 + ln x6 - 2 ln (2x)
1. ln 4
2. ln 2
3. ln x
4. ln (2x)

4. . What is 3 ln x2 + 2 ln y - 5 ln z3 when expressed as a single term?

1. ln (x2 + y - z3)
2. ln (3x2 + 2y - 5z3)
3. ln [x6y2/z15]
4. ln [6x2y/5z3]

5. . What is the expanded form of the natural logarithm below?

ln (6x3/y2 z)
1. 3 ln (6x) - 2 ln y - ln z
2. 18 ln x - 2 ln y + ln z
3. 18 ln x - 2 ln y - ln z
4. 9 ln x - ln y + ln z

6. . What is

eln 2x + 2 ∙ (ln x2 - 1/2 ln x3 )
1. 2x - ln x
2. ln (2x) + ln x
3. 2 ln x
4. ln x

7. . If we take ln 2 = 0.7, ln 3 = 1.1 and ln 5 = 1.6, then what is ln 30?

1. e30
2. 1.232
3. 0.943
4. 3.4

8. . What is the value of x in the equation below to one decimal place?

52x = 5e
1. 0.8
2. 0.9
3. 1.6
4. 3.2

9. . What is the value of x in the equation

ln x + ln (x - 3) = ln 10
1. -2
2. 5
3. 6.5
4. -2 and 5

10. . What is the function represented by the graph below?

1. y(x) = ln x
2. y(x) = ln (2x)
3. y(x) = 2 ln x
4. y(x) = ln x2

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