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Mathematics
Mathematics
Problem
Let
g
(
x
)
=
5
⋅
10
2
x
−
1
g(x)=5\cdot 10^{2x-1}
g
(
x
)
=
5
⋅
1
0
2
x
−
1
for real
x
x
x
. a. (i) Rewrite
g
(
x
)
g(x)
g
(
x
)
in the form
k
a
x
k\,a^{x}
k
a
x
, where
k
k
k
and
a
a
a
are positive constants independent of
x
x
x
. b. (ii) Find
g
′
(
x
)
g'(x)
g
′
(
x
)
. c. (iii) Evaluate
g
′
(
log
10
5
)
g'(\log_{10}5)
g
′
(
lo
g
10
5
)
. (Here
log
10
\log_{10}
lo
g
10
denotes the logarithm to base
10
10
10
.)
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