Basic Technical Mathematics, 11th Edition

Exercises 13.3, page 384

1. 1. ${\log }_{4}3\hspace{0.17em}+\hspace{0.17em}{\log }_{4}7$

2. 3. ${\log }_4\left({\displaystyle \frac{5}{x}}\right)$

3. 5. 3

4. 7. ${\displaystyle \frac{1}{2}}$

5. 9. ${\log }_{5}3\hspace{0.17em}+\hspace{0.17em}{\log }_{5}11$

6. 11. ${\log }_{7}9\hspace{0.17em}-\hspace{0.17em}{\log }_{7}2$

7. 13. $3{\log }_{2}a$

8. 15. ${\log }_{6}a\hspace{0.17em}+\hspace{0.17em}{\log }_{6}b\hspace{0.17em}+\hspace{0.17em}2{\log }_{6}c$

9. 17. $5{\log }_{5}t$

10. 19. ${\displaystyle \frac{1}{2}}{\log }_{2}x\hspace{0.17em}-\hspace{0.17em}2{\log }_{2}a$

11. 21. ${\log }_{\text{b}}ac$

12. 23. ${\log }_{5}3$

13. 25. ${\log }_{\text{b}}{x}^{\mathrm{5/2}}$

14. 27. ${\log }_{\text{e}}{\displaystyle \frac{4{\pi }^3}{3}}$

15. 29. $\hspace{0.17em}-\hspace{0.17em}5$

16. 31. 2.5

17. 33. 3

18. 35. 8

19. 37. $2\hspace{0.17em}+\hspace{0.17em}{\log }_{3}2$

20. 39. $2\hspace{0.17em}-\hspace{0.17em}{\log }_{2}7$

21. 41. ${\displaystyle \frac{1}{2}}(1\hspace{0.17em}+\hspace{0.17em}{\log }_{3}2)$

22. 43. $3\hspace{0.17em}+\hspace{0.17em}{\log }_{10}3$

23. 45. $y\hspace{0.17em}=\hspace{0.17em}2x$

24. 47. $y\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{3x}{5}}$

25. 49. $y\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{49}{x^3}}$

26. 51. $y\hspace{0.17em}=\hspace{0.17em}2{(2ax)}^{\mathrm{1/5}}$

27. 53. $y\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{2}{x}}$

28. 55. $y\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{x^2}{25}}$

29. 57. ${\log }_{10}x\hspace{0.17em}+\hspace{0.17em}{\log }_{10}3\hspace{0.17em}=\hspace{0.17em}{\log }_{10}3x$

30. 59. $y\hspace{0.17em}=\hspace{0.17em}{\log }_{\text{e}}(e^{2}x)\hspace{0.17em}=\hspace{0.17em}2{\log }_{\text{e}}e\hspace{0.17em}+\hspace{0.17em}{\log }_{\text{e}}x\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em}+\hspace{0.17em}{\log }_{\text{e}}x$

    

31. 61. 8

32. 63. 2x

33. 65. $y_1\hspace{0.17em}=\hspace{0.17em}{y}_2$

    

34. 67. $D\hspace{0.17em}=\hspace{0.17em}a{e}^{c{r}^2\hspace{0.17em}-\hspace{0.17em}br}$

35. 69. $T\hspace{0.17em}=\hspace{0.17em}90.0e^{\hspace{0.17em}-\hspace{0.17em}0.23t}$