- In your own words, explain the meaning of
25.Concept Check Based on the meaning of what is the simplest form of
26.A company has found that total sales, in thousands of dollars, are given by the function
defined by
where xis the number of weeks after a major advertising campaign was introduced.
(a)What were the total sales 6 weeks after the campaign was introduced?
(b) Graph the function.
10.4 Apply the properties of logarithms to express each logarithm as a sum or difference
of logarithms. Assume that all variables represent positive real numbers.
27. 28.
Apply the properties of logarithms to write each expression as a single logarithm. Assume that
all variables represent positive real numbers,
10.5 Evaluate each logarithm. Give approximations to four decimal places.
31.log 28.9 32.log 0.257 33.ln 28.9 34.ln 0.257
Use the change-of-base rule (with either common or natural logarithms) to find each logarithm.
Give approximations to four decimal places.
Use the formula to find the pHof each substance with the given hydronium
ion concentration.
37.Milk, 38.Crackers,
39.If orange juice has pH 4.6, what is its hydronium ion concentration?
40.The magnitude of a star is defined by the equation
where is the measure of the faintest star and Iis the actual intensity of the star being
measured. The dimmest stars are of magnitude 6, and the brightest are of magnitude 1.
Determine the ratio of intensities between stars of magnitude 1 and 3.
- Section 10.5, Exercise 42introduced the doubling function defined by
that gives the number of years required to double your money when it is invested at inter-
est rate r(in decimal form) compounded annually. How long does it take to double your
money at each rate? Round answers to the nearest year.
(a)4% (b) 6% (c)10% (d) 12%
(e) Compare each answer in parts (a) – (d) with the following numbers. What do you find?
72
4
,
72
6
,
72
10
,
72
12
t 1 r 2 =
ln 2
ln 11 +r 2
,
I 0
M= 6 - 2.5 log
I
I 0
,
4.0 10 -^7 3.8 10 -^9
pH=-log 3 H 3 O+ 4
log 16 13 log 4 12
logb 3 +logb x-2 logb y log 3 1 x+ 72 - log 3 14 x+ 62
bZ1.
log 4
2 x#w 2
z
log 2 3 xy^2
S 1 x 2 =100 log 2 1 x+ 22 ,
logb a, blogb^ a?
logb a.
628 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions
