The image shows four graphs of logarithmic functions. Each graph plots a function on a coordinate plane with x and y axes ranging from -5 to 5. The functions are labeled on the right side of the image:**Graphs and Functions:**1. **First Graph:** - **Function:** \( f(x) = -\log_3(x) \) - **Description:** The graph starts from negative infinity as x approaches zero from the positive side and increases, passing through the point (1, 0), eventually decreasing slowly as x increases.2. **Second Graph:** - **Function:** \( f(x) = \log_{\frac{2}{5}}(x) \) - **Description:** A decreasing logarithmic graph that starts from positive infinity as x approaches zero from the positive side and decreases, passing through the point (1, 0), eventually declining at a slow rate.3. **Third Graph:** - **Function:** \( f(x) = \log_2(x) \) - **Description:** An increasing logarithmic graph that starts from negative infinity as x approaches zero from the positive side and rises, passing through the point (1, 0), eventually increasing at a slower rate.4. **Fourth Graph:** - **Function:** \( f(x) = -\log_{\frac{2}{5}}(x) \) - **Description:** An increasing logarithmic graph where the function starts from negative infinity as x approaches zero from the positive side and rises, passing through the point (1, 0), eventually leveling off as x increases.Each graph is plotted on a grid with increments of 1 on both axes, represented with gridlines for clarity. The behavior of each function is typical of logarithmic functions, showing either an increasing or decreasing trend depending on the base and sign of the logarithm.

Answered: Image /qna-images/answer/9d154916-374c-483a-9ae3-258f144eec53.jpg

4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 5 4 3 2 1 -5 -4 -3 -2 -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 -5 -4 -3 -2 -1 5 4- 3 2 1 -1 -2 -3 -4 -5+ 5 + 4 3 2 1 -1 -2 1 2 3 4 1 2 3 3 3 5 4 5 a. f(x) = -log(x) b. f(x) = log₂ (x) c. f(x) = d. f(x) = log₂ (x) - logą (x)

4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 5 4 3 2 1 -5 -4 -3 -2 -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 -5 -4 -3 -2 -1 5 4- 3 2 1 -1 -2 -3 -4 -5+ 5 + 4 3 2 1 -1 -2 1 2 3 4 1 2 3 3 3 5 4 5 a. f(x) = -log(x) b. f(x) = log₂ (x) c. f(x) = d. f(x) = log₂ (x) - logą (x)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The image shows four graphs of logarithmic functions. Each graph plots a function on a coordinate plane with x and y axes ranging from -5 to 5. The functions are labeled on the right side of the image:

**Graphs and Functions:**

1. **First Graph:**
- **Function:** \( f(x) = -\log_3(x) \)
- **Description:** The graph starts from negative infinity as x approaches zero from the positive side and increases, passing through the point (1, 0), eventually decreasing slowly as x increases.

2. **Second Graph:**
- **Function:** \( f(x) = \log_{\frac{2}{5}}(x) \)
- **Description:** A decreasing logarithmic graph that starts from positive infinity as x approaches zero from the positive side and decreases, passing through the point (1, 0), eventually declining at a slow rate.

3. **Third Graph:**
- **Function:** \( f(x) = \log_2(x) \)
- **Description:** An increasing logarithmic graph that starts from negative infinity as x approaches zero from the positive side and rises, passing through the point (1, 0), eventually increasing at a slower rate.

4. **Fourth Graph:**
- **Function:** \( f(x) = -\log_{\frac{2}{5}}(x) \)
- **Description:** An increasing logarithmic graph where the function starts from negative infinity as x approaches zero from the positive side and rises, passing through the point (1, 0), eventually leveling off as x increases.

Each graph is plotted on a grid with increments of 1 on both axes, represented with gridlines for clarity. The behavior of each function is typical of logarithmic functions, showing either an increasing or decreasing trend depending on the base and sign of the logarithm.

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