Exponential And Logarithmic Equations Worksheet - Section 4-7
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11314
314
4 INVERSE FUNCTIONS; EXPONENTIAL AND LOGARITHMIC FUNCTIONS
4 INVERSE FUNCTIONS; EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Section 4-7 Exponential and Logarithmic Equations
Exponential Equations
Logarithmic Equations
Change of Base
Equations involving exponential and logarithmic functions, such as
3x 2
2
5
and
log (x
3)
log x
1
are called exponential and logarithmic equations, respectively. Logarithmic
properties play a central role in their solution. Of course, a graphing utility can
be used to find approximate solutions for many exponential and logarithmic equa-
tions. However, there are situations where the algebraic solution is necessary. In
this section, we emphasize algebraic solutions and use a graphing utility as a
check, when appropriate.
Exponential Equations
The following examples illustrate the use of logarithmic properties in solving
exponential equations.
E X A M P L E
Solving an Exponential Equation
1
3x 2
Solve 2
5 for x to four decimal places.
How can we get x out of the exponent? Use logs! Since the logarithm function
S o l u t i o n
is one-to-one, if two positive quantities are equal, their logs are equal. See The-
orem 1 in Section 4-5.
3x 2
2
5
3x 2
log 2
log 5
Take the common or natural log of
both sides.
p
Use log
N
p log
N to get
(3x
2) log 2
log 5
b
b
3x
2 out of the exponent position.
FIGURE 1
log 5
3x 2
y
2
, y
5.
3x
2
1
2
log 2
8
1
log 5
log 5
Remember:
log 5
log 2.
x
2
log 2
3
log 2
2
4
To four decimal places.
1.4406
Figure 1 shows a graphical solution that confirms this result.
0
1 2x
Solve 35
7 for x to four decimal places.
M A T C H E D P R O B L E M
1
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education