Title: Logarithms (Properties) Class: Math 107 or Math 111 or Math 120 or Math 137 Author: Lindsey Bramlett-Smith Instructions to Tutor: Read instructions and follow all steps for each problem exactly as given. Keywords/Tags: logarithms, properties of logarithms, logs, simplifying logarithms, rewriting logarithms Logarithms (Properties) Purpose: This is intended to refresh your skills in working with the properties of logarithms. This includes simplifying logarithms and rewriting logarithms. Activity: Work through the following activity and examples. Do all of the practice problems before consulting with a tutor. The rules that govern the use of logarithms can become “familiar” for two reasons: i) logarithms are exponents (so their rules are the rules of exponents)

ii) logarithms are functions (where b" log " is the name of the function)

(for example, 4 416 16 16 2f log log )

Basic Rules for Logarithms: for 0 1b , b , and 0 0m , n

1) b b blog mn log m log n

2) b b b

mlog log m log n

n

3) pb blog m p log m

2 2 22 8 2 8log log log 2 2 2

22 8

8log log log

8

2 22 8 2log log

2 16 1 3Verify : log 2

11 3

4Verify : log

2 256 8 1Verify : log

But not all logs can be rewritten. Some common mistakes:

b b blog m n log m log n ( blog is a function name, and we can not distribute function

names)

b b blog m log n log mn

bb

b

log m mlog

log n n

p pb b blog m p log m log m

Practice: Rewrite, then simplify:

5 25 25log 7

1

49log

3

7 7log

6 66 36log log 6 66 36log log 26 6log

Extended Questions:

6 6 36log 7

7

49

7

log

log

2

6 6log 6 536 25log log

(answer: 6 42log ) (answer: 2) (answer: 1) (answer: 4)

Review: Meet with a tutor to verify your work on this worksheet and discuss some of the areas that

were more challenging for you. If necessary, choose more problems from the homework to practice and discuss with the tutor.

For Tutor Use: Please check the appropriate statement: Student has completed worksheet but may need further assistance. Recommend a

follow-up with the instructor. Student has mastered topic.