Power Rule Properties of Logarithms - Ch 7 - Houston ISD

[Pages:7]Properties of Logarithms - Ch 7

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

1

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

2

Apply Properties of Logarithms Any base example

Common Log example Natural Log example

Apply Properties of Logarithms

Expanding Expressions Using Logarithmic Rules

Example #1

Apply Properties of Logarithms

Expanding Expressions Using Logarithmic Rules

Example #2

Apply Properties of Logarithms Expanding Expressions Using

Logarithmic Rules

Example #3

Apply Properties of Logarithms

Expanding Expressions Using Logarithmic Rules

Example #4

Apply Properties of Logarithms

Condensing Expressions Using Logarithmic Rules

Example #1

3

Apply Properties of Logarithms

Change of Base Formula

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

4

Properties of Logarithms 1

Name: ________________________

A2.A.19: Properties of Logarithms 1: Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms

1 The expression log 12 is equivalent to 1) log6 log 6 2) log3 2log2 3) log3 2log2 4) log3 log4

2 The expression log 4x is equivalent to 1) log x4 2) 4 log x 3) log4 log x 4) (log 4)(logx)

3 Which expression is not equivalent to logb 36? 1) 6 logb 2 2) logb 9 logb 4 3) 2 logb 6 4) logb 72 logb 2

4 If A r2 , log A equals 1) 2log logr 2) log 2 log r 3) 2log 2logr 4) 2 logr

5

If

L

x2 k

,

then

log L

is

equal

to

1)

2

log

x k

2) 2(logx log k)

3) 2log x log k

2log x 4) log k

6

The

expression

log

b3 a

is equivalent to

1) 3(log b loga)

2) log3b loga

3) 3log b loga

3log b 4) loga

7

If u

x y2

, which

expression is equivalent to

log u?

1) logx 2logy

2) 2(logx logy)

3) 2(logx logy)

4) logx 2logy

8 If log x2 log 2a log 3a , then log x expressed in

terms of log a is equivalent to

1)

1 2

log

5a

2)

1 2

log

6

log

a

3) log6 log a

4) log6 2 log a

9 The expression log xy is equivalent to

1) 2log x logy

2) 2(logx logy)

3)

1 2

log

x

log

y

4)

1 2

(log

x

log

y)

1

Regents Exam Questions A2.A.19: Properties of Logarithms 1



Name: ________________________

10 If x (82 )( 5 ), which expression is equivalent to

log x ?

1) 2log 8 2log 5

2)

2(log

8

1 2

log

5)

3)

2

log

8

1 2

log

5

4)

(2

log

8)(

1 3

log 5)

xy 13 The expression log w is equivalent to

2log xy 1) logw

2) logx log y logw

3)

1 2

(log

x

log

y)

log

w

4)

1 2

(log

xy

log

w)

11 If x a c b , then log x is equal to

1)

log a

1 2

log b

log c

2) loga 2log b log c

3)

log a

1 2

log b

log c

4) loga 2log b log c

xy 12 Log z is equal to

1)

1 2

log x

1 2

log y

log z

2)

1 2

log

x

log

y

log

z

3)

1 2

??? log

x

log

y

log

z

^?~

1 2

log

xy

4) log z

14 Log

a b

is equivalent to

1)

1 2

log

a

log

b

2)

1 2

(log

a

log

b)

3)

1 2

(log

a

log

b)

4)

1 2

log

a

log

b

15

The expression log??????????

xn y

^?~~~~~~~~

is equivalent to

1)

n

log

x

1 2

log

y

2) n logx 2logy

3)

log(nx)

log???????

1 2

y

^?~~~~~

4) log(nx) log(2y)

2

Regents Exam Questions A2.A.19: Properties of Logarithms 1



Name: ________________________

16

The

expression

log??????????

x2y3 z

^?~~~~~~~~

is

equivalent

to

(2x)(3y)

1)

1 2

z

2)

2log x

3log y

1 2

log z

3)

log

2x

log

3y

log

1 2

z

4)

2

log

x

3

log

y

1 2

log

z

x2y3 17 The expression log z is equivalent to

1)

1 2

(2

log

x

3

log

y

log

z)

2)

1 2

(2

log

x

3

log

y)

log

z

3) 2log x 3logy log z

x2y3 4) z

19

If r 3

A2B C

,

then

log r

can

be

represented

by

1)

1 6

log A

1 3

log B

log C

2) 3(log A2 log B log C)

3)

1 3

log(A2

B)

C

4)

2 3

log

A

1 3

log

B

1 3

log

C

4 x2y 20 The equation N z is equivalent to

1)

log N

1 4

(2 log x

log y

logz)

2)

log N

1 4

(2 log x

log y)

log z

3)

log N

1 4

log 2x

1 4

log y

logz

4)

log N

2 4

log x

1 4

log(y

z)

3a 18 The expression log b is equivalent to

1)

1 3

log

a

log

b

2)

1 3

log(a

b)

3) 3log a logb

4) 3log(a b)

21

The expression log 4

a2 b

is equivalent to

1)

1 4

??????????

log a 2 log b

^?~~~~~~~~

2) 4(log a 2 log b)

3)

1 2

(4

log

a

log

b)

4)

1 4

(2

log

a

log

b)

22 Log cot A is equivalent to 1) logsinA logcos A 2) logsinA logcos A 3) logcos A logsinA 4) logcos A logsinA

3

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