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Mathematics LibreTexts

4.4E: Logarithmic Properties (Exercises)

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section 4.4 exercise

Simplify to a single logarithm, using logarithm properties.

1. log3(28)log3(7)

2. log3(32)log3(4)

3. log3(17)

4. log4(15)

5. log3(110)+log3(50)

6. log4(3)+log4(7)

7. 13log7(8)

8. 12log5(36)

9. log(2x4)+log(3x5)

10. ln(4x2)+ln(3x3)

11. ln(6x9)ln(3x2)

12. log(12x4)log(4x)

13. 2log(x)+3log(x+1)

14. 3log(x)+2log(x2)

15. log(x)12log(y)+3log(z)

16. 2log(x)+13log(y)log(z)

Use logarithm properties to expand each expression.

17. log(x15y13z19)

18. log(a2b3c5)

19. ln(a2b4c5)

20. ln(a2b3c5)

21. log(x3y4)

22. log(x3y2)

23. ln(yy1y)

24. ln(x1x2)

25. log(x2y33x2y5)

26. log(x3y47x3y9)

Solve each equation for the variable.

27. 44x7=39x6

28. 22x5=73x7

29. 17(1.14)x=19(1.16)x

30. 20(1.07)x=8(1.13)x

31. 5e0.12t=10e0.08t

32. 3e0.09t=e0.14t

33. log2(7x+6)=3

34. log3(2x+4)=2

35. 2ln(3x)+3=1

36. 4ln(5x)+5=2

37. log(x3)=2

38. log(x5)=3

39. log(x)+log(x+3)=3

40. log(x+4)+log(x)=9

41. log(x+4)log(x+3)=1

42. log(x+5)log(x+2)=2

43. log6(x2)log6(x+1)=1

44. log3(x2)log3(x+2)=5

45. log(x+12)=log(x)+log(12)

46. log(x+15)=log(x)+log(15)

47. ln(x)+ln(x3)=ln(7x)

48. ln(x)+ln(x6)=ln(6x)

Answer

1. log3(4)

3. log3(7)

5. log3(5)

7. log7(2)

9. log(6x9)

11. ln(2x7)

13. log(x2(x+1)3)

15. log(xz3y)

17. 15log(x)+13log(y)19log(z)

19. 2ln(a)+4ln(b)5ln(c)

21. 32log(x)2log(y)

23. ln(y)+12(ln(y)ln(1y))

25. 83log(x)+143log(y)

27. x0.717

29. x6.395

31. t17.329

33. x=27

35. x0.123

37. x4.642

39. x30.158

41. x2.889

43. x6.873 or x0.873

45. x=12111.091

47. x=10


This page titled 4.4E: Logarithmic Properties (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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