Power Rule Properties of Logarithms - Ch 7...Regents Exam Questions A2.A.19: Properties of...
Transcript of Power Rule Properties of Logarithms - Ch 7...Regents Exam Questions A2.A.19: Properties of...
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Apply Properties of Logarithms
4.5 Apply Properties of Logarithms
• Product Property
• Quotient Property
• Power Property
• Inverse Property
• Change of Base Formula
Apply Properties of Logarithms
Product Rule
Apply Properties of Logarithms
Any base example
Common Log example
Natural Log example
Apply Properties of Logarithms
Quotient Rule
Apply Properties of Logarithms
Any base example
Common Log example
Natural Log example
Apply Properties of Logarithms
Power Rule
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Apply Properties of Logarithms
Any base example
Common Log example
Natural Log example
Apply Properties of Logarithms
Other Rules Part 1
Apply Properties of Logarithms
Any base example
Common Log example
Natural Log example
Apply Properties of Logarithms
Other Rules Part 2
Apply Properties of Logarithms
Any base example
Common Log example
Natural Log example
Apply Properties of Logarithms
Other Rules Part 3
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Apply Properties of Logarithms
Any base example
Common Log example
Natural Log example
Apply Properties of LogarithmsExpanding Expressions Using
Logarithmic RulesExample #1
Apply Properties of LogarithmsExpanding Expressions Using
Logarithmic RulesExample #2
Apply Properties of LogarithmsExpanding Expressions Using
Logarithmic RulesExample #3
Apply Properties of LogarithmsExpanding Expressions Using
Logarithmic RulesExample #4
Apply Properties of Logarithms
Condensing Expressions Using Logarithmic Rules
Example #1
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Apply Properties of Logarithms
Change of BaseFormula
Apply Properties of Logarithms
Apply Properties of Logarithms
4.5 Apply Properties of Logarithms
• Product Property
• Quotient Property
• Power Property
• Inverse Property
• Change of Base Formula
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A2.A.19: Properties of Logarithms 1: Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms
1 The expression log12 is equivalent to1) log6 log62) log3 2log23) log3 2log24) log3 log4
2 The expression log4x is equivalent to
1) logx 4
2) 4logx3) log4 logx4) (log4)(logx)
3 Which expression is not equivalent to logb 36?
1) 6logb 2
2) logb 9 logb 4
3) 2logb 6
4) logb 72 logb 2
4 If A r2 , logA equals1) 2log logr2) log 2logr3) 2log 2logr4) 2 logr
5 If L x 2
k, then logL is equal to
1) 2logxk
2) 2(logx logk)3) 2logx logk
4)2logxlogk
6 The expression logb 3
a is equivalent to
1) 3(logb loga)2) log3b loga3) 3logb loga
4)3logbloga
7 If u x
y 2 , which expression is equivalent to logu?
1) logx 2logy2) 2(logx logy)3) 2(logx logy)4) logx 2logy
8 If logx 2 log2a log3a , then logx expressed in terms of loga is equivalent to
1)12
log5a
2)12
log6 loga
3) log6 loga4) log6 2loga
9 The expression log xy is equivalent to
1) 2logx logy2) 2(logx logy)
3)12
logx logy
4)12
(logx logy)
Properties of Logarithms 1 Name: ________________________
Regents Exam Questions A2.A.19: Properties of Logarithms 1 Name: ________________________ www.jmap.org
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10 If x (82 )( 5), which expression is equivalent to logx?1) 2log8 2log5
2) 2(log8 12
log5)
3) 2log8 12
log5
4) (2log8)(13
log5)
11 If x a b
c, then logx is equal to
1) loga 12
logb logc
2) loga 2logb logc
3) loga 12
logb logc
4) loga 2logb logc
12 Logxy
z is equal to
1)12
logx 12
logy logz
2)12
logx logy logz
3)12
logx logy logzÊËÁÁ
ˆ¯̃̃
4)
12
logxy
logz
13 The expression logxy
w is equivalent to
1)2logxylogw
2) logx logy logw
3)12
(logx logy) logw
4)12
(logxy logw)
14 Logab
is equivalent to
1)12
loga logb
2)12
(loga logb)
3)12
(loga logb)
4)12
loga logb
15 The expression logxn
y
Ê
Ë
ÁÁÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃˜̃
is equivalent to
1) n logx 12
logy
2) n logx 2logy
3) log(nx) log12
yÊ
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
4) log(nx) log(2y)
Regents Exam Questions A2.A.19: Properties of Logarithms 1 Name: ________________________ www.jmap.org
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16 The expression logx 2 y 3
z
Ê
Ë
ÁÁÁÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃˜̃̃ is equivalent to
1)(2x)(3y)
12
z
2) 2logx 3logy 12
logz
3) log2x log3y log12
z
4) 2logx 3logy 12
logz
17 The expression logx2 y 3
z is equivalent to
1)12
(2logx 3logy logz)
2)12
(2logx 3logy) logz
3) 2logx 3logy logz
4)x 2 y3
z
18 The expression loga3
b is equivalent to
1)13
loga logb
2)13
log(a b)
3) 3loga logb4) 3log(a b)
19 If r A2 BC
3 , then logr can be represented by
1)16
logA 13
logB logC
2) 3(logA2 logB logC)
3)13
log(A2 B) C
4)23
logA 13
logB 13
logC
20 The equation N x 2 y4
z is equivalent to
1) logN 14
(2logx logy logz)
2) logN 14
(2logx logy) logz
3) logN 14
log2x 14
logy logz
4) logN 24
logx 14
log(y z)
21 The expression loga 2
b4 is equivalent to
1)14
loga 2
logb
Ê
Ë
ÁÁÁÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃˜̃̃
2) 4(loga 2 logb)
3)12
(4loga logb)
4)14
(2loga logb)
22 LogcotA is equivalent to1) logsinA logcos A2) logsinA logcos A3) logcos A logsinA4) logcos A logsinA