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Mathematics LibreTexts

4.5E: Graphs of Logarithmic Functions (Exercises)

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section 4.5 exercise

For each function, find the domain and the vertical asymptote.

1. f(x)=log(x5)

2. f(x)=log(x+2)

3. f(x)=ln(3x)

4. f(x)=ln(5x)

5. f(x)=log(3x+1)

6. f(x)=log(2x+5)

7. f(x)=3log(x)+2

8. f(x)=2log(x)+1

Sketch a graph of each pair of functions.

9. f(x)=log(x),g(x)=ln(x)

10. f(x)=log2(x),g(x)=log4(x)

Sketch each transformation.

11. f(x)=2log(x)

12. f(x)=3ln(x)

13. f(x)=ln(x)

14. f(x)=log(x)

15. f(x)=log2(x+2)

16. f\left(x\right)=\log _{3} \left(x+4\right)\]

Find a formula for the transformed logarithm graph shown.

17. 屏幕快照 2019-06-26 下午6.26.37.png18. 屏幕快照 2019-06-26 下午6.28.07.png

19. 屏幕快照 2019-06-26 下午6.28.25.png20. 屏幕快照 2019-06-26 下午6.28.40.png

Find a formula for the transformed logarithm graph shown.

21. 屏幕快照 2019-06-26 下午6.29.08.png22.屏幕快照 2019-06-26 下午6.29.26.png

23. 屏幕快照 2019-06-26 下午6.29.43.png24.屏幕快照 2019-06-26 下午6.30.01.png

Answer

1. Domain: x>5 V. A. @ x=5

3. Domain: x<5 V. A. @ x=3

5. Domain: x>13 V. A. @ x=13

7. Domain: x<0 V. A. @ x=0

9. Screen Shot 2019-10-04 at 2.47.23 PM.png

11. Screen Shot 2019-10-04 at 2.47.40 PM.png

13. Screen Shot 2019-10-04 at 2.47.56 PM.png

15. Screen Shot 2019-10-04 at 2.48.16 PM.png

17. y=1log(2)log((x1))

19. y=3log(3)log(x+4)

21. y=3log(4)log(x+2)

23. y=2log(5)log((x5))


This page titled 4.5E: Graphs of Logarithmic Functions (Exercises) is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by David Lippman & Melonie Rasmussen (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform.

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