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Byju's Answer
Standard XII
Mathematics
Average Rate of Change
If x change...
Question
If
x
changes from
4
to
4.01
then find the approximate change in
l
o
g
x
.
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Solution
Given,
x
=
4
On taking
l
o
g
both sides, we get
l
o
g
x
=
l
o
g
4
...... (1)
Now,
x
+
δ
x
=
4.01
On taking
l
o
g
both sides, we get
l
o
g
(
x
+
δ
x
)
=
l
o
g
4.01
......(2)
Divide both equations such that
e
q
u
a
t
i
o
n
(
2
)
e
q
u
a
t
i
o
n
(
1
)
, we get
l
o
g
(
x
+
δ
x
)
l
o
g
x
=
l
o
g
(
4.01
)
l
o
g
4
l
o
g
(
x
+
δ
x
−
x
)
=
l
o
g
(
4.01
−
4
)
[from the properties of
l
o
g
]
l
o
g
(
x
+
δ
x
−
x
)
=
l
o
g
(
0.01
)
l
o
g
δ
x
=
l
o
g
(
10
)
−
2
l
o
g
δ
x
=
−
2
l
o
g
10
=
−
2
×
1
=
−
2.
Hence, this is the answer.
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