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Trashketball Review

Chapter 3
Exponents and Logarithms
Trashketball
      Review of ch 4
1    6 11 16 21 26 31
2    7 12 17 22 27 32
3    8 13 18 23 28 33
4    9 14 19 24 29 34
5   10 15 20 25 30 35
1
    Solve.
      52x = 59x + 7

             x = -1
2
    Solve.
             2
         x        6          3x 4
     4                   4
                 x = -2, 5
3
    Solve.
             3x 2    1
       16
                    64
             x=1
               6
4
    Solve.
       27x = 800

         x = 1.378
5
    Solve.
      logx 512 = 3

             x=8
6
        Solve.
    log8 (3x - 6) = log8 (9x + 23)

                    29
             x
                    6
7
     Solve.
    log7   (x2   - 5) = log7 (59)

             x        8
8
    Solve.
    log9(x + 3) = log92x

             x=3
9
    Solve. Round to 4 decimal places.

            3x = 72

           x = 3.8928
10
     Solve. Round to 4 decimal places   .


         7x = 23.4

           x = 1.6202
11
     Solve. Round to 4 decimal places.
           53x = 37

            x = 0.7479
12
     Write in logarithmic form.
           82 = 64

          log8 64 = 2
13
     Write in logarithmic form.
           93 = 729

          log9 729 = 3
14
     Solve for x.
         log x = -2

            10-2 = x
            0.01 = x
15
     Solve for x.
         logx 4 = 12


           x = 1.122
16
     Write in exponential form.
                1
        log13         3
              2197

             3     1
        13
                 2197
17
     Write in exponential form.
         log11 1331 = 3

          113 = 1331
18
     Solve for x.

        42x   =   5x-1


           x = -1.38
19
     Solve for x.
       42x - 5 · 4x - 14 = 0


           x = 1.404
20
     Evaluate
                 1
          log 7
                2401

                -4
21
     Evaluate
           log15 225


                2
22
     Evaluate
          log 6 1296

                4
23
     Expand
          log3   (27x)2


     2(log3 27 + log3 x)
     = 2log327 + 2log3x
24
     Expand
                  x
              log
                  9
         log x – log 9
25
     Express as single logarithm
                    1
      log x 3 log y   log z
                    3
                   3
               xy
           log 3
                 z
26
     Express as single logarithm
         1
           log 25 5 log a
         2
                    5
            log5a
27
     Evaluate. Round to 4 decimal places.
              log11 52

                1.6478
28
     Evaluate. Round to 4 decimal places.
              log5 8.7

                1.3441
29
     Evaluate. Round to 4 decimal places.
             log6 21.7

                1.7175
30
     Evaluate. Round to 4 decimal places.
             log13 28.3

                1.3033
31
     Solve
      log(x+3) = 1 – log(x)

             X=2
32
      Solve

     log(x+45) – log(x+5) = log x

              X=5
33
     If you invest some money at a
     5.5% rate compounded
     continuously, how long will it
     take to double?
                 12.6 years
34
     You invest $1500 at a 4.9% interest
     rate compounded quarterly. How
     much will you have in 3 years?


                $1735.98
35


       A certain city has a population of 4000
     people in 1990 and 4500 people in 2000.
     Find an exponential function to model this
     population. Then predict the population in
                        2015.
               y = 4000e.0118t

                  13018 people

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Ch 3 rev trashketball exp logs

  • 2. Trashketball Review of ch 4 1 6 11 16 21 26 31 2 7 12 17 22 27 32 3 8 13 18 23 28 33 4 9 14 19 24 29 34 5 10 15 20 25 30 35
  • 3. 1 Solve. 52x = 59x + 7 x = -1
  • 4. 2 Solve. 2 x 6 3x 4 4 4 x = -2, 5
  • 5. 3 Solve. 3x 2 1 16 64 x=1 6
  • 6. 4 Solve. 27x = 800 x = 1.378
  • 7. 5 Solve. logx 512 = 3 x=8
  • 8. 6 Solve. log8 (3x - 6) = log8 (9x + 23) 29 x 6
  • 9. 7 Solve. log7 (x2 - 5) = log7 (59) x 8
  • 10. 8 Solve. log9(x + 3) = log92x x=3
  • 11. 9 Solve. Round to 4 decimal places. 3x = 72 x = 3.8928
  • 12. 10 Solve. Round to 4 decimal places . 7x = 23.4 x = 1.6202
  • 13. 11 Solve. Round to 4 decimal places. 53x = 37 x = 0.7479
  • 14. 12 Write in logarithmic form. 82 = 64 log8 64 = 2
  • 15. 13 Write in logarithmic form. 93 = 729 log9 729 = 3
  • 16. 14 Solve for x. log x = -2 10-2 = x 0.01 = x
  • 17. 15 Solve for x. logx 4 = 12 x = 1.122
  • 18. 16 Write in exponential form. 1 log13 3 2197 3 1 13 2197
  • 19. 17 Write in exponential form. log11 1331 = 3 113 = 1331
  • 20. 18 Solve for x. 42x = 5x-1 x = -1.38
  • 21. 19 Solve for x. 42x - 5 · 4x - 14 = 0 x = 1.404
  • 22. 20 Evaluate 1 log 7 2401 -4
  • 23. 21 Evaluate log15 225 2
  • 24. 22 Evaluate log 6 1296 4
  • 25. 23 Expand log3 (27x)2 2(log3 27 + log3 x) = 2log327 + 2log3x
  • 26. 24 Expand x log 9 log x – log 9
  • 27. 25 Express as single logarithm 1 log x 3 log y log z 3 3 xy log 3 z
  • 28. 26 Express as single logarithm 1 log 25 5 log a 2 5 log5a
  • 29. 27 Evaluate. Round to 4 decimal places. log11 52 1.6478
  • 30. 28 Evaluate. Round to 4 decimal places. log5 8.7 1.3441
  • 31. 29 Evaluate. Round to 4 decimal places. log6 21.7 1.7175
  • 32. 30 Evaluate. Round to 4 decimal places. log13 28.3 1.3033
  • 33. 31 Solve log(x+3) = 1 – log(x) X=2
  • 34. 32 Solve log(x+45) – log(x+5) = log x X=5
  • 35. 33 If you invest some money at a 5.5% rate compounded continuously, how long will it take to double? 12.6 years
  • 36. 34 You invest $1500 at a 4.9% interest rate compounded quarterly. How much will you have in 3 years? $1735.98
  • 37. 35 A certain city has a population of 4000 people in 1990 and 4500 people in 2000. Find an exponential function to model this population. Then predict the population in 2015. y = 4000e.0118t 13018 people