Math 083 – Intermediate Algebra                                                         NAME

Mrs. Donna Tupper                                                                              Quiz 4

Fall 2001

 

 

Answer each question below and show all work were applicable.  You will NEED to use your calculator for most of this test!

1.  Let f(x) = 2^x.  Evaluate each of the following.  This question is worth 20 points, 5 points for each part.

 

 

a]  f(0) =

 

 

 

 

 

 

b]  f(-3) =

 

 

 

 

 

 

c]  f(5) =

 

 

 

 

 

 

d]  f(1/3)

 

 

 

 

 

 

 

 

 

 

2.  On the graph paper below, graph f(x) = 2^x).  For your convenience, a table is below for you to put in your values of x and f(x).  This question is worth 10 points.  5 points for the correct table and 5 for the correct graph.  You may use your TABLE and GRAPH utilities on your TI-83 if you have one.  If not, then do the work by hand.

 

x y
   
   
   
   

 

 

 

 

3.  Use the formula

coversion

to express each of the following in logarithmic form.  This question is worth 10 points, 5 points for each part.

 

 

 

A]  4^3 = 64

 

 

B]  2^(-3) = 1/8

 

 

 

 

 

4.  Use the formula

to express each of the following in exponential form. This question is worth 10 points, 5 points for each part.

 

 

 

 

A]  log (base 10) of 1000 = 3

 

 

 

 

 

B]  log (base 2) 128 = 7

 

 

 

 

 

 

 

 

5.  Use the properties of logarithms (listed on the attached sheet) to expand each expression as much as possible.  This question is worth 10 points, 5 points for each part.

 

 

 

 

A]  log (to base 3) (x / 2y)

 

 

 

 

 

B]  log (base of 5) (x^2y^4z^2)

 

 

 

 

 

 

 

 

 

6.     Use the properties of logarithms (again use the attached sheet) to write each expression as a single logarithm.  This question is worth 10 points, 5 points for each part.

 

 

A]  6 log x - 2 log y

 

 

 

 

 

 

B]  log x + 3 log y - 2 log z

 

 

 

 

 

 

 

 

 

 

 

7.  Solve the logarithmic equation  log (base of 3) (3x) = 3.  This question is worth 10 points.

 

 

 

 

 

 

 

 

 

 

 

 

8.  Use your calculator to determine each of the following.  Round each answer off to 2 decimal places.  This question is worth 20 points.  Each part is worth 2 points each.

 

 

 

A]  log 235

 

 

B]  log 1.4

 

 

C]  log 27,000

 

 

D]  ln e

 

 

E]  ln 3

 

 

F]  ln (e^(-3))

 

 

G]  ln (e^(5/2))

 

 

H]  ln(3/7)

 

 

I]  ln  225

 

 

 

J]  ln  0

 

 

 

 

Click here for answers.