Questions Attached

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For Problems 1 – 6, rewrite in equivalent exponential form.

1.

A logarithmic expression of the form can be written in equivalent exponential form as .

Applying this to the given expression gives:

The remaining problems in this section use the same format.

2.

3.

4.

5.

6.

In Problems 7 – 12, rewrite in equivalent logarithmic form.

8.

This is the reverse of the problems in the preceding section. These expressions have the form . The equivalent logarithmic equation has the form

.

Applying this to the given equation gives:

The remaining problems follow the same format.

9.

11.

In Problems 13 – 20, evaluate the expression without using a calculator.

13.

14.

17.

19.

20.

33 = 27

3

3

=27

log2 32 = 5

log

2

32=5

25 = 32

2

5

=32

log101= 0

log

10

1=0

100 =1

10

0

=1

loge1= 0

log

e

1=0

e0 =1

e

0

=1

log4 8 = 3 2

log

4

8=

3

2

4 3 2 = 8

4

3

2

=8

log9 27 = 3 2

log

9

27=

3

2

9 3 2 = 27

9

3

2

=27

36 = 62

36=6

2

a = bx

a=b

x

logb a = x

log

b

a=x

log6 36 = 2

log

6

36=2

8 = 4 3 2

8=4

3

2

log4 8 = 3 2

log

4

8=

3

2

A = bu

A=b

u

logb A = u

log

b

A=u

log10100 = log10 10 2( ) = 2*log1010 = 2*1= 2

log

10

100=log

10

10

2

()

=2*log

10

10=2*1=2

log327 = 3

log

3

27=3

log10100,000 = log10 10 5( ) = 5*log1010 = 5*1= 5

log

10

100,000=log

10

10

5

()

=5*log

10

10=5*1=5

log5 1 25

= log5 5 −2( ) = −2*log5 5 = −2*1= −2

log

5

1

25

=log

5

5

-2

()

=-2*log

5

5=-2*1=-2

ln 1 e4

⎛ ⎝⎜

⎞ ⎠⎟ = ln e−4( ) = −4*ln e( ) = −4*1= −4

ln

1

e

4

æ

è

ç

ö

ø

÷

=lne

-4

()

=-4*lne

()

=-4*1=-4

ln e−5( ) = −5*ln e( ) = −5*1= −5

lne

-5

()

=-5*lne

()

=-5*1=-5

logb a = x

log

b

a=x

bx = a

b

x

=a