College Algebra, 2013a

456 Exponential and Logarithmic Functions
6.3.1 Exercises
In Exercises 1 - 33, solve the equation analytically.
1. 2 4x = 8 2. 3 (x−1) =27 3. 5 2x−1 = 125
4. 4 2x = 1 2
5. 8 x = 1
128
6. 2 (x3 −x) =1
7. 3 7x =81 4−2x 8. 9 · 3 7x = ( 1
9) 2x
9. 3 2x =5
10. 5 −x = 2 11. 5 x = −2 12. 3 (x−1) =29
13. (1.005) 12x = 3 14. e −5730k = 1 2
15. 2000e 0.1t = 4000
16. 500 ( 1 − e 2x) = 250 17. 70 + 90e −0.1t = 75 18. 30 − 6e −0.1x =20
100e x
19.
e x +2 =50 20. 5000
1+2e −3t = 2500 21. 150
1+29e
22. 25 ( )
4 x
5 = 10 23. e 2x =2e x 24. 7e 2x =28e −6x
25. 3 (x−1) =2 x 26. 3 (x−1) = ( )
1 (x+5)
27. 7 3+7x =3 4−2x
2
−0.8t
=75
28. e 2x − 3e x − 10 = 0 29. e 2x = e x + 6 30. 4 x +2 x =12
31. e x − 3e −x = 2 32. e x +15e −x = 8 33. 3 x +25· 3 −x =10
In Exercises 34 - 39, solve the inequality analytically.
34. e x > 53 35. 1000 (1.005) 12t ≥ 3000
36. 2 (x3 −x) < 1 37. 25 ( 4
5) x ≥ 10
150
38.
1+29e −0.8t ≤ 130 39. 70 + 90e−0.1t ≤ 75
In Exercises 40 - 45, use your calculator to help you solve the equation or inequality.
40. 2 x = x 2 41. e x =ln(x) + 5 42. e √x = x +1
43. e −x − xe −x ≥ 0 44. 3 (x−1) < 2 x 45. e x