(c)
Write with the same base.Power rule for exponentsSet exponents equal.Check that the solution set is 5 - 26. NOW TRY
x=- 2
a
2
3
b
x= a
2
3
b
- 2
a
2
3
b
x= ca
2
3
b
2d
- 1
9
4 =A4
9 Ba^2 -^1
3
b
x= a
4
9
b
- 1
a
2
3
b
x=
9
4
584 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions
NOTE The steps used in Examples 4 and 5cannot be applied to an equation like
because Step 1 cannot easily be done. A method for solving such exponential equa-
tions is given in Section 10.6.
3 x = 12
OBJECTIVE 4 Use exponential functions in applications involving growth
or decay.
Solving an Application Involving Exponential GrowthThe graph in FIGURE 8shows the concentration of carbon dioxide (in parts per mil-
lion) in the air. This concentration is increasing exponentially.
EXAMPLE 6
Carbon Dioxide in the Air
3901750 1800 1850 1900 1950 2000 205 0
Year0370
350
330
310
290
270Source: Sacramento Bee; National Oceanic and
Atmospheric Administration.Atmospheric CO2Concentration
(in parts per million)FIGURE 8The data are approximated by the function defined by
where xis the number of years since 1750. Use this function and a calculator to
approximate the concentration of carbon dioxide in parts per million, to the nearest
unit, for each year.
ƒ 1 x 2 = 2661 1.001 2 x,
NOW TRY
EXERCISE 5
Solve each equation.
(a)
(b)
(c) a
2
7
bx
=343
8
5 x=1
625
32 x-^1 = 27 x+^4NOW TRY ANSWERS
- (a) (b)
(c) 5 - 36
5 - 136 5 - 46