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# 4.5E: Graphs of Logarithmic Functions (Exercises)

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## Section 4.5 Exercises

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. 321

Section 4.6 Exponential and Logarithmic Models