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Properties of Logarithms

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

Summary: This module provides sample problems which develop concepts related to properties of logarithms.

Exercise 1

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

Exercise 2

log 2 ( 2 * 2 ) = log 2 (2*2)=

Exercise 3

log 2 ( 2 * 2 * 2 ) = log 2 (2*2*2)=

Exercise 4

log 2 ( 2 * 2 * 2 * 2 ) = log 2 (2*2*2*2)=

Exercise 5

log 2 ( 2 * 2 * 2 * 2 * 2 ) = log 2 (2*2*2*2*2)=

Exercise 6

Based on exercises #1-5, finish this sentence in words: when you take log 2 log 2 of a number, you find:

Exercise 7

log 2 ( 8 ) = log 2 (8)=

Exercise 8

log 2 ( 16 ) = log 2 (16)=

Exercise 9

log 2 ( 8 * 16 ) = log 2 (8*16)=

Exercise 10

log 3 ( 9 ) = log 3 (9)=

Exercise 11

log 3 ( 27 ) = log 3 (27)=

Exercise 12

log 3 ( 9 * 27 ) = log 3 (9*27)=

Exercise 13

Based on exercises #7-12, write an algebraic generalization about logs.

Exercise 14

Now, let’s dig more deeply into that one. Rewrite exercises #7-9 so they look like exercises #1-5: that is, so the thing you are taking the log of is written as a power of 2.

  • a. #7:
  • b. #8:
  • c. #9:
  • d. Based on this rewriting, can you explain why your generalization from #13 works?

Exercise 15

log 5 ( 25 ) = log 5 (25)=

Exercise 16

log 5 ( 1 25 ) = log 5 ( 1 25 )=

Exercise 17

log 2 ( 32 ) = log 2 (32)=

Exercise 18

log 2 ( 1 32 ) = log 2 ( 1 32 )=

Exercise 19

Based on exercises #15-18, write an algebraic generalization about logs.

Exercise 20

log 3 ( 81 ) = log 3 (81)=

Exercise 21

log 3 ( 81 * 81 ) = log 3 (81*81)=

Exercise 22

log 3 812 3 81 2

Exercise 23

log 3 ( 81 * 81 * 81 ) = log 3 (81*81*81)=

Exercise 24

log 3 813 3 81 3

Exercise 25

log 3 ( 81 * 81 * 81 * 81 ) = log 3 (81*81*81*81)=

Exercise 26

log 3 814 3 81 4

Exercise 27

Based on exercises #20-26, write an algebraic generalization about logs.

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