Page 45.

1. $x^8$
2. $x^6$
3. $x^{12}$
4. $x^{14}$
5. $8x^{10}$
6. $25 x^{13}$
7. $\tfrac{3}{2} x$
8. $40x$
9. $\tfrac{4}{x}$
10. $\tfrac{2}{x^5}$
11. $\tfrac{1}{x^2}$
12. $\tfrac{1}{x}$
13. $\tfrac{5}{2}x^3$

14. $\tfrac{1}{3x^2}$

    Problems 15 to 20 should read Rewrite using *positive* or fractional exponents

15. $4x^5$
16. $4x^3$
17. $3x^{1/2}$
18. $x^{1/4}$
19. $4x^{-1/3}$
20. $\tfrac{1}{5}x^{-1/2}$
21. $\tfrac{4}{\sqrt{x}}$
22. $\tfrac{5}{\sqrt[3]{x}}$
23. $2\sqrt[3]{x}$
24. $5\sqrt{x^3} = 5x\sqrt{x}$

Page 72

1. $10^t=v$
2. $10^s=r$
3. $e^n=w$
4. $e^y=x$
5. $\log b = a$
6. $\log v = p$
7. $\ln h = k$
8. $\ln x = y$
9. $x = \log_5 14$
10. $x = \log_3 23$
11. $x = -\log_7 15$
12. $x = -\log_3 4$
13. $x = \tfrac{1}{5}\ln 17$
14. $x = \tfrac{3}\ln 12$
15. $x = \tfrac{1}{4}\big( 5 + \log_3 38 \big)$
16. $x = \tfrac{1}{2} \big( 3 + \log_4 44 \big)$
17. $t = \log_{1.04} 5$
18. $t = \log_{1.06} 2.75$
19. $t = \tfrac{1}{3} \log_{1.04} \tfrac{8}{3}$
20. $t = \tfrac{1}{4} \log_{1.08} \tfrac{7}{2}$
21. $t = -\tfrac{1}{0.12} \ln 0.2$
22. $t = -\tfrac{1}{0.003} \ln 0.4$
23. $t = \log_{0.5} 0.635$
24. $t = \log_{0.25} 0.3$
25. In 2013
26. In 2026
27. About 13 months and two weeks
28. About 13 months