SKILLS
3-10 Exponential Equations Find the solution of the exponential equation, as in Example 1.
3. 5^{x-1} = 125
4. e^{x^2} = e^9
5. 5^{2x-3} = 1
6. 10^{2x-3} = 1/10
7. 7^{2x-3} = 7^{6+5x}
8. e^{1-2x} = e^{3x-5}
9. 6^{x^2-1} = 6^{1-x^2}
10. 10^{2x^2-3} = 10^{9-x^2}
11-38 Exponential Equations (a) Find the exact solution of the exponential equation in terms of logarithms. (b) Use a calculator to find an approximation to the solution rounded to six decimal places.
11. 10^x = 25
12. 10^{-x} = 4
13. e^{-5x} = 10
14. e^{0.4x} = 8
15. 2^{1-x} = 3
16. 3^{2x-1} = 5
17. 3e^x = 10
18. 2e^{12x} = 17
19. 300(1.025)^{12t} = 1000
20. 10(1.375)^{10t} =
21. e^{1-4x} = 2
22. e^{3-5x} = 16
23. 2^{5-7x} = 15
24. 2^{3x} = 34
25. 3^{x/14} = 0.1
26. 5^{-x/100} = 2
27. 4(1 + 10^{5x}) = 9
28. 2(5 + 3^{x+1}) =
29. 8 + e^{1-4x} = 20
30. 1 + e^{4x+1} =
31. 4^x + 2^{1+2x} = 50
32. 125^x + 5^{3x+1} =
33. 5^x - 4^{x+1} =
34. 10^{1-x} =