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Mathematics
Mathematics
Problem
Consider the function
g
(
x
)
=
e
a
x
+
2
g(x)=e^{ax}+2
g
(
x
)
=
e
a
x
+
2
defined on the closed interval
[
ln
2
,
ln
8
]
[\ln 2,\,\ln 8]
[
ln
2
,
ln
8
]
, where
a
a
a
is a non-zero real constant. The average value of
g
g
g
over this interval must equal
9
9
9
. Solve for the constant
a
a
a
. Clearly justify each step of your solution.
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