handa (nh5757) – Exponentials (1.5) – bormashenko – (54880)
1
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10
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001
10.0 points
Find the solution of the exponential equa
tion
4
7
x
= 16
1
2
x
+6
.
1.
x
= 2
correct
2.
x
=

2
3.
x
=
12
7
4.
x
=

12
7
5.
none of these
Explanation:
By properties of exponents,
16
1
2
x
+6
= 4
x
+12
.
Thus the equation can be rewritten as
4
7
x
= 4
x
+12
,
which after taking logs to the base 4 of both
sides becomes
7
x
=
x
+ 12
.
Rearranging and solving we thus find that
x
= 2
.
002
10.0 points
Find
x
when
2
x
= 8
y
,
4
x
= 16
y

1
.
1.
x
=

6
correct
2.
none of these
3.
x
= 6
4.
x
= 2
5.
x
=

2
Explanation:
The equations
2
x
= 8
y
,
4
x
= 16
y

1
are equivalent to
2
x
= 2
3
y
,
2
2
x
= 2
4(
y

1)
.
Now set
v
= 2
x
and
u
= 2
y
. Then
v
=
u
3
,
v
2
=
1
16
u
4
.
Substituting for
u
in the second equation we
thus get
v
2
=
1
16
v
4
3
,
i
.
e
.,
v
= 2

6
.
Consequently, since
v
= 2
x
,
x
=

6
.
003
10.0 points
Determine which, if any, of the following
f
(
x
) = 25
x
+ 10
,
g
(
x
) = 5
2
x
+2
,
h
(
x
) = 25 (25
x
)
,
define the same function.
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 Spring '10
 Gualdini
 Exponential Function, Derivative, Exponentiation, Exponentials

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