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Mathematics
Problem
Let
y
=
x
2
(
3
x
−
1
)
5
1
+
x
4
y = x^{2}(3x-1)^{5}\sqrt{1+x^{4}}
y
=
x
2
(
3
x
−
1
)
5
1
+
x
4
for
x
>
0
x>0
x
>
0
. Which of the following expressions is equivalent to
ln
y
\ln y
ln
y
? a)
2
ln
x
+
5
ln
(
3
x
−
1
)
+
ln
(
1
+
x
4
)
2\ln x + 5\ln(3x-1) + \ln(1+x^{4})
2
ln
x
+
5
ln
(
3
x
−
1
)
+
ln
(
1
+
x
4
)
b)
ln
x
+
5
ln
(
3
x
−
1
)
+
1
2
ln
(
1
+
x
4
)
\ln x + 5\ln(3x-1) + \dfrac{1}{2}\ln(1+x^{4})
ln
x
+
5
ln
(
3
x
−
1
)
+
2
1
ln
(
1
+
x
4
)
c)
2
ln
x
+
5
ln
(
3
x
−
1
)
+
1
2
ln
(
1
+
x
4
)
2\ln x + 5\ln(3x-1) + \dfrac{1}{2}\ln(1+x^{4})
2
ln
x
+
5
ln
(
3
x
−
1
)
+
2
1
ln
(
1
+
x
4
)
d)
2
ln
x
+
1
5
ln
(
3
x
−
1
)
+
1
2
ln
(
1
+
x
4
)
2\ln x + \dfrac{1}{5}\ln(3x-1) + \dfrac{1}{2}\ln(1+x^{4})
2
ln
x
+
5
1
ln
(
3
x
−
1
)
+
2
1
ln
(
1
+
x
4
)
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