Exponential And Logarithmic Equations Worksheet - Section 4-7 Page 3
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4 INVERSE FUNCTIONS; EXPONENTIAL AND LOGARITHMIC FUNCTIONS
0.21x
7.35
14.7e
0.21x
Divide both sides by 14.7 to simplify.
0.5
e
0.21x
Since the base is e, take the natural log of both
ln 0.5
ln e
FIGURE 3
sides.
0.21x
y
14.7e
, y
7.35.
1
2
In e
1
0.21x
20
ln 0.5
x
0.21
0
5
To two significant digits.
3.3 miles
Figure 3 shows that this answer is correct.
0
Using the formula in Example 3, find the altitude in miles so that the atmospheric
M A T C H E D P R O B L E M
3
pressure will be one-eighth that at sea level. Compute the answer to two signifi-
cant digits.
The graph of
x
x
e
e
y
(1)
2
is a curve called a catenary (Fig. 4). A uniform cable suspended between two
fixed points is a physical example of such a curve.
x
x
FIGURE 4
e
e
y
y
Catenary.
2
10
5
x
5
5
E X A M P L E
Solving an Exponential Equation
4
Given equation (1), find x for y
2.5. Compute the answer to four dec-
imal places.
x
x
e
e
y
S o l u t i o n
2
x
x
e
e
2.5
2
x
x
5
e
e
x
x
2x
Multiply both sides by e
.
5e
e
1
x
2x
x
This is a quadratic in e
.
e
5e
1
0
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