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(a−2b−4c5)
20. ln(a−2b3c−5)
21. log(√x3y−4)
22. log(√x−3y2)
23. ln(y√y1−y)
24. ln(x√1−x2)
25. log(x2y33√x2y5)
26. log(x3y47√x3y9)
Solve each equation for the variable.
27. 44x−7=39x−6
28. 22x−5=73x−7
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(x−3)=ln(7x)
48. ln(x)+ln(x−6)=ln(6x)
- Answer
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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(xz3√y)
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(1−y))
25. 83log(x)+143log(y)
27. x≈−0.717
29. x≈−6.395
31. t≈17.329
33. x=27
35. x≈0.123
37. x≈4.642
39. x≈30.158
41. x≈−2.889
43. x≈6.873 or x≈−0.873
45. x=1211≈1.091
47. x=10