Section 8.6
Properties of Logarithms; Solving Exponential Equations
841
Version: Fall 2007
8.6
Exercises
In
Exercises 1

10
, use a calculator to
evaluate the function at the given value
p
.
Round your answer to the nearest
hundredth.
1.
f
(
x
) = log
4
(
x
)
;
p
= 57
.
60
.
2.
f
(
x
) = log
4
(
x
)
;
p
= 11
.
22
.
3.
f
(
x
) = log
7
(
x
)
;
p
= 2
.
98
.
4.
f
(
x
) = log
3
(
x
)
;
p
= 2
.
27
.
5.
f
(
x
) = log
6
(
x
)
;
p
= 2
.
56
.
6.
f
(
x
) = log
8
(
x
)
;
p
= 289
.
27
.
7.
f
(
x
) = log
8
(
x
)
;
p
= 302
.
67
.
8.
f
(
x
) = log
5
(
x
)
;
p
= 15
.
70
.
9.
f
(
x
) = log
8
(
x
)
;
p
= 46
.
13
.
10.
f
(
x
) = log
4
(
x
)
;
p
= 15
.
59
.
In
Exercises 11

18
, perform each of the
following tasks.
a) Approximate the solution of the given
equation using your graphing calcu
lator.
Load each side of the equa
tion into the
Y=
menu of your calcu
lator. Adjust the
WINDOW
parameters
so that the point of intersection of
the graphs is visible in the viewing
window.
Use the
intersect
utility
in the
CALC
menu of your calculator
to determine the xcoordinate of the
point of intersection. Then make an
accurate copy of the image in your
viewing window on your homework
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1
paper.
b) Solve the given equation algebraically,
and round your answer to the nearest
hundredth.
11.
20 = 3(1
.
2)
x
12.
15 = 2(1
.
8)
x
13.
14 = 1
.
4
5
x
14.
16 = 1
.
8
4
x
15.
−
4 = 0
.
2
x
−
9
16.
12 = 2
.
9
x
+ 2
17.
13 = 0
.
1
x
+1
18.
19 = 1
.
2
x
−
6
In
Exercises 19

34
, solve the given equa
tion algebraically, and round your an
swer to the nearest hundredth.
19.
20 =
e
x
−
3
20.
−
4 =
e
x
−
9
21.
23 = 0
.
9
x
+ 9
22.
10 =
e
x
+ 7
23.
19 =
e
x
+ 5
24.
4 = 7(2
.
3)
x
25.
18 =
e
x
+4
26.
15 =
e
x
+6
27.
8 = 2
.
7
3
x
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842
Chapter 8
Exponential and Logarithmic Functions
Version: Fall 2007
28.
7 =
e
x
+1
29.
7 = 1
.
1
8
x
30.
6 = 0
.
2
x
−
8
31.
−
7 = 1
.
3
x
−
9
32.
11 = 3(0
.
7)
x
33.
23 =
e
x
+ 9
34.
20 = 3
.
2
x
+1
35.
Suppose that you invest $17,000 at
6% interest compounded daily. How many
years will it take for your investment to
double? Round your answer to the near
est hundredth.
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 Natural logarithm, Logarithm

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