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