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