CP Pre‐Calc I  6.1: nth Root Functions   Halldorson 

A.  Evaluate each of the following without a calculator   1.  1

364       

2.  1236  

   

3.  3 125−        

4.  4 16      

B.  Rewrite each with a radical sign   5. 

( )1

2 4x  6.  1

6m      

C.   Rewrite without a radical sign   7.  23w   8.  3 w  

    

D. Graph 

14( )f x x=  and 

13( )g x x=  on the same window.  For what values of x is: 

  

  9.  f(x)<g(x)  10. f(x)>g(x)  11.  f(x)=g(x)     

 

CP Pre‐Calculus I  6.2: Rational Power Functions  Halldorson 

A.  Evaluate each of the following.  Show all work.   1.  3 0.027   2.  3

2425

⎛ ⎞⎜ ⎟⎝ ⎠

 

    

3.  161

64

−⎛ ⎞⎜ ⎟⎝ ⎠

 4. 

318

−  

   

B.  Solve for x  

  5.  2 16x =     

6.  8 16x =  

7. 

( )2726 x=  

  

8.  23 27 x−=  

 

LOGARITHMS PRACTICE WORKSHEET NO CALCULATORS!!!

Find each logarithm: 1. log2 64 4. log 104

2. log4 2 5. log1/3 181

3. log4 1

16 6. log1/4 64

Find the value of x in each equation: 7. logx 625 = 4 13. log (x2 + 9x) = 1 8. log25 x = ½ 14. log (4x – 4) = 2 9. log1/2 x = -6 15. log5 x = 3 log5 7 10. logx .1 = -1 16. log2 x = ½ log2 81 11. logx 125 = -3 17. log5 x = 2 log5 7

12. log√3 27 = x 18. log10 x = 16

(2 log 4 + 2 log 2)

Express each logarithm as the sum or difference of simpler logs: 19. log2 (xy) = 20. log2 (abc) = 21. loga 2x1/2 = 22. loga (bc)2 = 23. loga bc =

24. logb (x

y) =

Express each as a single logarithm with a coefficient of 1: 25. loga x + loga y – loga z = 26. 2 loga x – ½ loga y = 27. 2(loga z – loga 3) = Simplify (WITHOUT A CALCULATOR):

28. log6 2 + log6 3 29. log5 200 – log5 8 30. log 85 – log 17 + ½ log 400

8Name ________________________________ Logarithm Practice Worksheet Simplify WITHOUT a calculator:

1. 231000 2. 3 69 9⋅ 3. log3 9

4. ( ) 334 5. log9 3 6. log4 8

7. 2532

− 8. log10 .0001 9. ( )( )2 16 6π π− +

10. log2 8 11. log8 ½ 12. log9 27

13. log8 4 2 14. log4 x = 3 15. logx 8 = 34

Suppose f(x) = 1 – x3 and g(x) = 2x – 3. Find the following: 16. f(g(1)) 17. g(f(-1)) 18. f-1(9) 19. g-1(0) 20. f(f-1(4)) 21. g-1(f-1(0)) If log 5 = a and log 4 = b, express the logarithm in terms of a and b. Ex. log 16 = log 42 = 2log 4 = 2b

22. log 416

23. log 20 24. log 1.25

25. log 2 26. log 10 27. log 125

28. log 250 29. log 10 30. log 3 50

Let x = log 2, y = log 3, and z = log 10. Express each logarithm in terms of x, y, and z. 31. log 6 32. log 9 33. log 5 34. log 18 35. log 1.5 36. log .75 37. log 80 38. log 30 39. log .0006

40. log 92

41. log 1200

Let log a = 2, log b = 3, and log c = 4. Evaluate each logarithm.

42. log a2b 43. 3 2bc 44. log abc

45. log 6 2 3a b c 46. log 3 2

4

a bc

47. log 2

2

abc

Simplify to help you solve each equation.

48. log3 x + log3 15

= 0

49. 2log4 y = 3

50. If log8 5 = a, then log8 15

= _________

PRECALC I – SECTION 6.5 WORKSHEET USING PROPERTIES OF LOGS

EXPRESS THE FOLLOWING IN TERMS OF a, b, and c,

GIVEN: log 2 = a log 3 = b log 5 = c

1. log 4 =

2.log 25 =

3. log 10 =

4. log 6 =

5.log 15 =

6. log 95

=

7. log 4 3 =

8. log 3 25 =

9. log 3

25

=

10. log 6 =

 

Chapter 6 Guided Notes Halldorson 2009-2010

1

PRECALC I CHAPTER 6 STUDY GUIDE

1. Know how to simplify exponential and logarithmic expressions with and without a calculator. (#1-8, 17-22, 25, 26)

2. Know the properties of logs. (#37-43, 47, 48)

3. Be able to solve equations. (#13-16)

4. Know what the graphs exponential and logarithmic functions look like. Know the characteristics, like domain, range, asymptotes. (#30, 32-34, 69, 70)

5. Be able to give formulas in terms of another variable and then substitute in values. (#55a, 56, 59, 62)

6. Be able to solve compound interest problems and population problems. (#58, 60)  

PRECALC I – CHAPTER 6 REVIEW WORKSHEET 

SIMPLIFY EACH OF THE FOLLOWING WITHOUT A CALCULATOR 

1.  4

532          2.  4

327        3.  1

2125

−⎛ ⎞⎜ ⎟⎝ ⎠

   

 

4.  2

3827

−⎛ ⎞⎜ ⎟⎝ ⎠

        5.   6log 1      6.   10ln e  

 

7.   ( )15

log 25         8.  2log 8       9.   9

1log27

⎛ ⎞⎜ ⎟⎝ ⎠

         

 

 

10.   ( )( )136 15x y  

Chapter 6 Guided Notes Halldorson 2009-2010

2

 

EXPRESS EACH OF THE GIVEN LOGARITHMS AS THE SUM AND/OR DIFFERENCE OF SIMPLIER LOGS, WITHOUT ANY RADICALS OR EXPONENTS 

11. ( )3log ab c             12.   2ln xy

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

 

 

EXPRESS EACH OF THE FOLLOWING AS A SINGLE LOGARITHM WITH A COEFFICIENT OF ONE 

 

13.   log log 3logx y z+ −         14.   ( )2 ln ln 3p −  

 

15.  Express this equation without logs:   log log log 5 log 2 logx y w z− = + −  

 

16.  Determine the value of x (correct to the nearest thousandth):   ln 2x =  

 

17.  Determine the exact value of x:   274log

3x −=  

 

18.  Determine the exact value of m:   log 8 6m =  

 

MATCH EACH EQUATION WITH ITS GRAPH 

19.   ( ) xxf ln−=             20.   ( ) xxg 2=             21.   ( ) xxh 2log=             22.   ( ) ( )xxr 2.0=  

a.   b.    c.    d.   

 

   

4

2

-2

4

2

-2

-4

5

4

2

-2

4

2

-2

5

Chapter 6 Guided Notes Halldorson 2009-2010

3

23.  Matt invested $1,000.00 in an account paying 7.5% interest.  Determine his balance after four years if interest is: 

  a.  compounded monthly        b.  compounded continuously 

 

24.  Nicole has invested $5000 in an account paying 6.25% interest compounded continuously.  How long before her investment doubles in value? 

 

25.  In 1995 the population of Mexico was estimated at 94,800,000 with an annual growth rate of 1.85%.  Assuming continuous growth at this rate, estimate the population of Mexico in the year 2010. 

 

26.  The population of Peru in 1998 was estimated at 18,4000,000 with an annual average growth rate of 2.7%.  Assuming continuous growth at this rate, in what year would the population reach 30,000,000. 

 

SOLVE EACH OF THE EQUATIONS 

27.   ( ) 19log49log 66 =+x       28.  84 =x        29.  x

x ⎟⎠⎞

⎜⎝⎛=+

25125 2        

 

30.   212 279 ++ = xx         31.   25log4log −=−x   32.   ( ) ( ) 21ln1ln −=+−− xx  

 

 

FOR EACH OF THE GIVN FUNCTIONS: a). DRAW AN ACCURATE GRAPH, b).  STATE THE DOMAIN, c).  STATE THE RANGE, AND d).  STATE THE EQUATION OF ANY ASYMPTOTE(S). 

33.   ( ) xxg 3log=           34.   ( ) xxr 4=  

 

           

10

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

10

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Chapter 6 Guided Notes Halldorson 2009-2010

4

SOLVE EACH OF THE GIVEN EQUATIONS, CORREST TO THE NEAREST THOUSANDTH. 

35.   414.26 =x       36.   ( ) 40008.115 1 =−x       37.   80062

=xe      

   

 

EVALUATE EACH OF THE FOLLOWING WITHOUT A CALCULATOR, GIVEN THAT: 

8log 5 x=  AND  8log 12 y=  

38.   8log 60             39.   8log 144  

 

40.   8log 2.4             41.   8log 300  

 

 

EVALUATE EACH OF THE FOLLOWING (round your answer to the nearest thousandth). 

 

42.   6log 344             43.   ( )415log 20π  

 

44.  The altitude above sea level h (in feet) as a function of barometric pressure p (in lb/in2) can be approximated by the 

formula  28,300 ln14.7

ph ⎛ ⎞= − ⎜ ⎟⎝ ⎠

.  What is the altitude of Santa Fe, New Mexico, if the average barometric pressure 

there is about 11.5 lb/sec2?