Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 4.5
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Logarithms!!
Logarithms – Expand as much as possible
Goal: Become comfortable using the various properties of algorithms, so that later you can solve equations with logs
1) “Expand” as much as possible, using the product rule:
log 4 3  10
2) “Expand” as much as possible, using the quotient rule:
 27 
log 2  
 5 
3) “Expand” as much as possible, using the power rule:
log 6 x 7
Logarithms – Using the product, quotient, power rules for logarithms: 'Expand' the expression
Goal: Become comfortable using the various properties of algorithms, so that later you can solve equations with logs
4) “Expand” as much as possible:
log 8
x
13
5) “Expand” as much as possible:
log 9 10(4) 6
6) “Expand” as much as possible:
 27 
log 2  
 5 
7) “Expand” as much as possible:
log 6 x 7
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 4.5
Page 2 / 4
8)
d6
log 3
a  54
9) “Expand” as much as possible:
log 4 3  10
10) “Expand” as much as possible:
d6
log 3
a  54
Logarithms – Using the product, quotient, power rules for logarithms: 'Un-expand' the expression
Goal: Become comfortable using the various properties of algorithms, so that later you can solve equations with logs
11) “Un-Expand” as much as possible, so that you write the word log as few times as possible:
log 5 2  log 5 3
12) “Un-Expand” as much as possible, so that you write the word log as few times as possible:
log 2 9  log 2 5
13) “Un-Expand” as much as possible, so that you write the word log as few times as possible:
2 log 9 z  log 9 z  2
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 4.5
Page 3 / 4
14) “Un-Expand” as much as possible, so that you write the word log as few times as possible:
2log 5 p  log 5 3
15) “Un-Expand” as much as possible, so that you write the word log as few times as possible:
log 5 2  log 5 3
16) “Un-Expand” as much as possible, so that you write the word log as few times as possible:
log 2 9  log 2 5
17) “Un-Expand” as much as possible, so that you write the word log as few times as possible:
2 log 9 z  log 9 z  2
18) “Un-Expand” as much as possible, so that you write the word log as few times as possible:
2log 5 p  log 5 3
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 4.5
Page 4 / 4
Logarithms – Change of base
Goal: Find numeric values of logarithms that have weird bases
19) Use the change of base formula to find
20) Use the change of base formula to find the
the value of the following. Round the
value of the following. Round the ANSWER to 4
ANSWER to 4 decimal places:
decimal places:
log 3 56
log 2 21
21) Use the change of base formula to find
the value of the following. Round the
ANSWER to 4 decimal places:
22) Use the change of base formula to find the
value of the following. Round the ANSWER to 4
decimal places:
log 5 63
log 4 11
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