Intermediate Algebra (11th edition)

58.To solve the equation , we must find the exponent to which 5 must be raised in

order to obtain 7. This is.

(a)Use the change-of-base rule and your calculator to find.

(b)Raise 5 to the number you found in part (a). What is your result?

(c)Using as many decimal places as your calculator gives, write the solution set of

. (Equations of this type will be studied in more detail in Section 10.6.)
59.Let mbe the number of letters in your first name, and let nbe the number of letters in your
last name.
(a)In your own words, explain what means.
(b)Use your calculator to find.
(c)Raise mto the power indicated by the number found in part (b). What is your result?
60.The value of ecan be expressed as

Approximate eusing two terms of this expression, then three terms, four terms, five

terms, and six terms. How close is the approximation to the value of

with six terms? Does this infinite sum approach the value of every quickly?

Solve each application of a logarithmic function ( from Exercises 61 and 62of Section 10.3).

61.For 1981–2003, the number of billion cubic feet of natural gas gross withdrawals from

crude oil wells in the United States can be approximated by the function defined by

where represents 1981, represents 1982, and so on. (Source:Energy Infor-

mation Administration.) Use this function to approximate the number of cubic feet with-

drawn in 2003, to the nearest unit.

62.According to selected figures from the last two decades of the 20th century, the number of

trillion cubic feet of dry natural gas consumed worldwide can be approximated by the

function defined by

where represents 1980, represents 1981, and so on. (Source:Energy Infor-

mation Administration.) Use this function to approximate consumption in 2003, to the

nearest hundredth.

x= 1 x= 2

ƒ 1 x 2 =51.47+6.044 log 2 x,

x= 1 x= 2

ƒ 1 x 2 = 3800 +585 log 2 x,

eL2.718281828

e= 1 +

1

1

+

1

1 # 2

+

1

1 # 2 # 3

+

1

1 # 2 # 3 # 4

+Á.

logm n

logm n

5 x= 7

log 5 7

log 5 7

5 x= 7

612 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions

Solve each equation. See Sections 10.2 and 10.3.

65. 66.

67. 68.

Write as a single logarithm. Assume See Section 10.4.

69.log 1 x+ 22 +log 1 x+ 32 70.log 4 1 x+ 42 - 2 log 4 13 x+ 12

x 7 0.

log1/2 8 =x loga 1 = 0

log 3 1 x+ 42 = 2 logx 64 = 2

25 x=a

1

16

b

x+ 3

42 x= 83 x+^1

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