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Problems
Mathematics
Mathematics
Problem
If for
x
,
y
∈
R
,
x
>
0
x, y \in R, x > 0
x
,
y
∈
R
,
x
>
0
,
y
=
log
10
x
+
log
10
x
1
/
3
+
log
10
x
1
/
9
+
…
y = \log_{10} x + \log_{10} x^{1/3} + \log_{10} x^{1/9} + \dots
y
=
lo
g
10
x
+
lo
g
10
x
1/3
+
lo
g
10
x
1/9
+
…
upto
∞
\infty
∞
terms and
2
+
4
+
6
+
⋯
+
2
y
3
+
6
+
9
+
⋯
+
3
y
=
4
log
10
x
\frac{2+4+6+\dots+2y}{3+6+9+\dots+3y} = \frac{4}{\log_{10} x}
3
+
6
+
9
+
⋯
+
3
y
2
+
4
+
6
+
⋯
+
2
y
=
l
o
g
10
x
4
, then the ordered pair
(
x
,
y
)
(x, y)
(
x
,
y
)
is equal to: (A)
(
10
6
,
6
)
(10^6, 6)
(
1
0
6
,
6
)
(B)
(
10
4
,
6
)
(10^4, 6)
(
1
0
4
,
6
)
(C)
(
10
2
,
3
)
(10^2, 3)
(
1
0
2
,
3
)
(D)
(
10
6
,
9
)
(10^6, 9)
(
1
0
6
,
9
)
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