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Homework: Logs

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems related to logarithms.

log 2 8 log 2 8 asks the question: “2 to what power is 8?” Based on that, you can answer the following questions:

Exercise 1

log 2 8 = log 2 8=

Exercise 2

log 3 9 = log 3 9=

Exercise 3

log 10 10 = log 10 10=

Exercise 4

log 10 100 = log 10 100=

Exercise 5

log 10 1000 = log 10 1000=

Exercise 6

log 10 1,000,000 = log 10 1,000,000=

Exercise 7

Looking at your answers to exercises #3-6, what does the log 10 log 10 tell you about a number?

Exercise 8

Multiple choice: which of the following is closest to log 10 500 log 10 500 ?

  • A. 1
  • B. 1 1 2 1 1 2
  • C. 2
  • D. 2 1 2 2 1 2
  • E. 3

Exercise 9

log 10 1 = log 10 1=

Exercise 10

log 10 1 10 = log 10 1 10 =

Exercise 11

log 10 1 100 = log 10 1 100 =

Exercise 12

log 2 (0.01) = log 2 (0.01)=

Exercise 13

log 10 0 = log 10 0=

Exercise 14

log 10 (-1) = log 10 (-1)=

Exercise 15

log 9 81 = log 9 81=

Exercise 16

log 9 1 9 = log 9 1 9 =

Exercise 17

log 9 3 = log 9 3=

Exercise 18

log 9 1 81 = log 9 1 81 =

Exercise 19

log 9 1 3 = log 9 1 3 =

Exercise 20

log 5 (54) = log 5 (54)=

Exercise 21

5log54= 5log54 size 12{5 rSup { size 8{"log" rSub { size 6{5} } 4} } } {}=

OK. When I say 3636 size 12{ sqrt {"36"} } {} = 6 =6, that’s the same thing as saying 6 2 = 36 6 2 =36. Why? Because 3636 size 12{ sqrt {"36"} } {} asks a question: “What squared equals 36?” So the equation 3636 size 12{ sqrt {"36"} } {}= 6 =6 is providing an answer: “six squared equals 36.”

You can look at logs in a similar way. If I say log 2 32 = 5 log 2 32=5 I’m asking a question: “2 to what power is 32?” And I’m answering: “two to the fifth power is 32.” So saying log 2 32 = 5 log 2 32=5 is the same thing as saying 2 5 = 32 2 5 =32.

Based on this kind of reasoning, rewrite the following logarithm statements as exponent statements.

Exercise 22

log 2 8 = 3 log 2 8=3

Exercise 23

log 3 1 3 = -1 log 3 1 3 =-1

Exercise 24

log x (1) = 0 log x (1)=0

Exercise 25

log a x = y log a x=y

Now do the same thing backward: rewrite the following exponent statements as logarithm statements.

Exercise 26

4 3 = 64 4 3 =64

Exercise 27

8 - 2 3 = 1 4 8- 2 3 = 1 4

Exercise 28

a b = c a b =c

Finally...you don’t understand a function until you graph it...

Exercise 29

  • a. Draw a graph of y = log 2 x y= log 2 x . Plot at least 5 points to draw the graph.
  • b. What are the domain and range of the graph? What does that tell you about this function?

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