Intermediate Algebra (11th edition)

630 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions

Evaluate.

Solve.

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    73. 74.Consider the logarithmic equation
    
    
    
    

(a)Solve the equation using properties of logarithms.

(b)If and ,

then the graph of looks like that shown.

Explain how the display at the bottom of the

screen confirms the solution set found in part (a).

75.Based on selected figures from 1980 through 2007, the fractional part (as a decimal) of

the generation of municipal solid waste recovered can be approximated by the function

defined by

where corresponds to 1980, to 1990, and so on. Based on this model,

approximate the percent, to the nearest hundredth, of municipal solid waste recovered

in 2005. (Source:U.S. Environmental Protection Agency.)

76.One measure of the diversity of the species in an ecological community is the index of

diversity,the logarithmic expression

where are the proportions of a sample belonging to each of nspecies in

the sample. (Source:Ludwig, John and James Reynolds, Statistical Ecology: A Primer

on Methods and Computing,New York, John Wiley and Sons.) Approximate the index

of diversity to the nearest thousandth if a sample of 100 from a community produces

the following numbers.

(a)90 of one species, 10 of another (b)60 of one species, 40 of another

p 1 , p 2 ,Á, pn

• 1 p 1 ln p 1 +p 2 ln p 2 +Á+pn ln pn 2 ,

x= 0 x= 10

R 1 x 2 =0.0997 1 e0.0470x 2 ,

Y 1 - Y 2

Y 1 =log 1 2X+ 32 Y 2 =log X+ 1

log 12 x+ 32 =log x+1.

log 13 x- 12 =log 10 ln 1 x^2 + 3 x+ 42 =ln 2

5 x+^2 = 252 x+^1 log 3 1 x+ 12 - log 3 x= 2

27 x= 81 22 x-^3 = 8

logx

1

81

log 31 x+ 92 = 4 ln ex= 3 = 2

10 log e log 3 3 -^5 ln e5.4

log 2 128 5 log^5 36 eln 4

1.Decide whether each function is one-to-one.

(a)ƒ 1 x 2 =x^2 + 9 (b)

TEST

CHAPTER 10

View the complete solutions to
all Chapter Test exercises on
the Video Resources on DVD.

Step-by-step test solutions are found on the Chapter Test Prep Videos

available via the Video Resources on DVD, in , or on

(search “LialIntermediateAlg”).

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MIXED REVIEW EXERCISES

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