Exponential And Logarithmic Equations Worksheet - Section 4-7 Page 4
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4-7 Exponential and Logarithmic Equations
x
Let u
e
, then
2
u
5u
1
0
5
25
4(1)(1)
u
2
5
21
2
5
21
x
x
e
Replace u with e
and solve for x.
2
Take the natural log of both sides
5
21
x
(both values on the right are
ln e
ln
FIGURE 5
2
positive).
x
x
e
e
y
, y
2.5
.
1
2
5
21
2
x
x
ln
log
b
x.
b
5
2
1.5668, 1.5668
5
5
Figure 5 confirms the positive solution. Note that the algebraic method also pro-
duced exact solutions, an important consideration in certain calculus applications
(see Problems 57–60 in Exercise 4-7).
0
x
x
Given y
(e
e
)/2, find x for y
1.5. Compute the answer to three
M A T C H E D P R O B L E M
4
decimal places.
2x
x
x
E x p l o r e / D i s c u s s
Let y
e
3e
e
(A) Try to find x when y
7 using the method of Example 4. Explain
the difficulty that arises.
1
(B) Use a graphing utility to find x when y
7.
Logarithmic Equations
We now illustrate the solution of several types of logarithmic equations.
E X A M P L E
Solving a Logarithmic Equation
5
Solve log (x
3)
log x
1, and check.
First use properties of logarithms to express the left side as a single logarithm,
S o l u t i o n
then convert to exponential form and solve for x.
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