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# 4.5.5E: Graphs of Logarithmic Functions (Exercises)

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section 4.5 exercise

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

1. $$f\left(x\right)=\log \left(x-5\right)$$

2. $$f\left(x\right)=\log \left(x+2\right)$$

3. $$f\left(x\right)=\ln \left(3-x\right)$$

4. $$f\left(x\right)=\ln \left(5-x\right)$$

5. $$f\left(x\right)=\log \left(3x+1\right)$$

6. $$f\left(x\right)=\log \left(2x+5\right)$$

7. $$f\left(x\right)=3\log \left(-x\right)+2$$

8. $$f\left(x\right)=2\log \left(-x\right)+1$$

Sketch a graph of each pair of functions.

9. $$f\left(x\right)=\log \left(x\right),\; g\left(x\right)=\ln \left(x\right)$$

10. $$f\left(x\right)=\log _{2} (x),\; g\left(x\right)=\log _{4} \left(x\right)$$

Sketch each transformation.

11. $$f\left(x\right)=2\log \left(x\right)$$

12. $$f\left(x\right)=3\ln \left(x\right)$$

13. $$f\left(x\right)=\ln \left(-x\right)$$

14. $$f\left(x\right)=-\log \left(x\right)$$

15. $$f\left(x\right)=\log _{2} (x+2)$$

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

Find a formula for the transformed logarithm graph shown.

17. 18.

19. 20.

Find a formula for the transformed logarithm graph shown.

21. 22.

23. 24.

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

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

5. Domain: $$x > -\dfrac{1}{3}$$ V. A. @ $$x = -\dfrac{1}{3}$$

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

9.

11.

13.

15.

17. $$y = \dfrac{1}{\text{log}(2)} \text{log} (-(x - 1))$$

19. $$y = -\dfrac{3}{\text{log}(3)} \text{log}(x + 4)$$

21. $$y = \dfrac{3}{\text{log}(4)} \text{log}(x + 2)$$

23. $$y = -\dfrac{2}{\text{log}(5)} \text{log}(-(x - 5))$$