Practice and Problem-Solving Exercises

See Problem 1.

A Practice

Solve each equation.

7. 2 x = 8 2 to the x , equals 8
8. 3 2 x = 27 3 super 2 x end super , equals 27
9. 4 3 x = 64 4 super 3 x end super , equals 64
10. 5 3 x = 1 125 5 super 3 x end super , equals , 1 over 125
11. 2 5 x + 1 = 32 2 super 5 x plus 1 end super . equals 32
12. 3 − 2 x + 2 = 81 3 super negative 2 x plus 2 end super . equals 81
13. 2 3 x = 4 x + 1 2 super 3 x end super , equals . 4 super x plus 1 end super
14. 3 x + 2 = 27 2 x 3 super x plus 2 end super . equals , 27 super 2 x end super

See Problem 2.

Solve each equation. Round to the nearest ten-thousandth.

Check your answers.

15. 2 x = 3 2 to the x , equals 3
16. 4 x = 19 4 to the x , equals 19
17. 8 + 10 x = 1008 8 plus , 10 to the x , equals , 1008
18. 5 − 3 x = − 40 5 minus , 3 to the x , equals negative 40
19. 9 2 y = 66 9 super 2 y end super , equals 66
20. 12 y − 2 = 20 12 super y minus 2 end super . equals 20
21. 25 2 x + 1 = 144 25 super 2 x plus 1 end super . equals 144
22. 2 3 x − 4 = 5 2 , 3 to the x , minus to the fourth . equals 5

See Problem 3.

Graphing Calculator Solve by graphing. Round to the nearest ten-thousandth.

23. 4 7 x = 250 4 super 7 x end super , equals 250
24. 5 3 x = 500 5 super 3 x end super , equals 500
25. 6 x = 4565 6 to the x , equals , 4565
26. 1 . 5 x = 356 1 . , 5 to the x , equals 356

Use a table to solve each equation. Round to the nearest hundredth.

27. 2 x + 3 = 512 2 super x plus 3 end super . equals 512
28. 3 x − 1 = 72 3 super x minus 1 end super . equals 72
29. 6 2 x = 10 6 super 2 x end super , equals 10
30. 5 2 x = 56 5 super 2 x end super , equals 56

    See Problem 4.

31. The equation : y = 6.72 ( 1.014 ) x colon y equals , 6.72 . open , 1.014 , close to the x  models the world population y, in billions of people, x years after the year 2000. Find the year in which the world population is about 8 billion.

See Problem 5.

Solve each equation. Check your answers.

32. log 2 x = − 1 log 2 x equals negative 1
33. 2 log x = − 1 2 log x equals negative 1
34. log ( 3 x + 1 ) = 2 log open 3 x plus 1 close equals 2
35. log x + 4 = 8 log x plus 4 equals 8
36. log 6 x − 3 = − 4 log 6 x minus 3 equals negative 4
37. 3 log x = 1.5 3 log x equals 1.5
38. 2 log ( x + 1 ) = 5 2 log open x plus 1 close equals 5
39. log ( 5 − 2 x ) = 0 log open 5 minus , 2 to the x , close equals 0

See Problem 6.

Solve each equation.

40. log x − log 3 = 8 log x minus log 3 equals 8
41. log 2 x + log x = 11 log 2 x plus log x equals 11
42. 2 log x + log 4 = 2 2 log x plus log 4 equals 2
43. log 5 − log 2 x = 1 log 5 minus log 2 x equals 1
44. 3 log x − log 6 + log 2.4 = 9 3 log x minus log 6 plus log , 2.4 equals 9
45. log ( 7 x + 1 ) = log ( x − 2 ) + 1 log open 7 x plus 1 close equals log open x minus 2 close plus 1

Table of Contents