OBJECTIVE 5 Use logarithmic functions in applications involving growth
or decay.
Solving an Application of a Logarithmic FunctionThe function defined by
approximates the barometric pressure in inches
of mercury at a distance of xmiles from the eye
of a typical hurricane. (Source:Miller, A. and
R. Anthes, Meteorology,Fifth Edition, Charles
E. Merrill Publishing Company.) Approximate
the pressure 9 mi from the eye of the hurricane.
Let and find
LetAdd inside parentheses.Add.The pressure 9 mi from the eye of the hurricane is 28.105 in. NOW TRY
ƒ 192 =28.105
ƒ 192 = 27 + 1.105 112 log 10 10 = 1
ƒ 192 = 27 + 1.105 log 10 10
ƒ 192 = 27 + 1.105 log 10 19 + 12 x=9.
x= 9, ƒ 192.
ƒ 1 x 2 = 27 +1.105 log 10 1 x+ 12
EXAMPLE 6
592 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions
Complete solution available
on the Video Resources on DVD
10.3 EXERCISES
1.Concept Check Match the logarithmic
equation in Column I with the corre-
sponding exponential equation from
Column II. See Example 1.
III
(a) A.(b) B.(c) C.(d) D.(e) E.(f ) F.2.Concept Check Match the logarithm
in Column I with its value in Column II.
(Example: because 2 is the
exponent to which 3 must be raised in
order to obtain 9.)
III
(a) A.
(b) B.(c) C. 2(d) D. 0(e) E.(f ) log 13 1 F. 41
2
log 525log 10 0.01log 3 a1
3
blog 3 81 - 1log 4 16 - 2log 3 9 = 2log 4 4 = 1 103 = 1000log 8238 = 50 = 11
3
log 10 1000 = 3 2 1/2= 22log 222 = 41 = 41
2
a1
3
b- 1
log 5 1 = 0 = 3
log1/3 3 =- 1 8 1/3= 238Write in logarithmic form. See Example 1.7. 8. 9. 10.
11. 12. 16 - 3/4= 13. 50 = 1 14. 70 = 1
1
8
8 - 2/3=
1
4
10 -^3 =0.001 36 1/2= 6 24625 = 5 23343 = 7
a1
6
b- 3
a = 216
1
2
b- 3
45 = 1024 36 = 729 = 8
NOW TRY
EXERCISE 6
Suppose the gross national
product (GNP) of a small
country (in millions of dol-
lars) is approximated by
where tis time in years since
- Approximate to the
nearest tenth the GNP for
each value of t.
(a)t= 1 (b)t= 10
G 1 t 2 =15.0+2.00 log 10 t,NOW TRY ANSWERS
- (a)$15.0 million
(b)$17.0 million