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Mathematics
Problem
Let
f
(
x
)
=
ln
x
f(x)=\ln x
f
(
x
)
=
ln
x
and
g
(
x
)
=
k
x
−
1
g(x)=kx-1
g
(
x
)
=
k
x
−
1
be defined on
[
1
,
e
]
[1,e]
[
1
,
e
]
, where
k
k
k
is a real parameter. For which of the following ranges of
k
k
k
is it guaranteed that
f
(
x
)
=
g
(
x
)
f(x)=g(x)
f
(
x
)
=
g
(
x
)
has at least one solution in
(
1
,
e
)
(1,e)
(
1
,
e
)
? a)
k
>
1
k>1
k
>
1
b)
2
e
<
k
<
1
\dfrac{2}{e}<k<1
e
2
<
k
<
1
c)
0
<
k
<
2
e
0<k<\dfrac{2}{e}
0
<
k
<
e
2
d)
k
<
0
k<0
k
<
0
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