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UPSC CDS Math Logarithm Questions
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© examsnet.com
Question : 4
Total: 16
Let XYZ be an equilateral triangle in which XY= 7 cm. If A denotes the area o f the triangle, then what is the value of
log
10
A
4
? (Given that
l
o
g
10
1050
=
3.0212
and
I
o
g
10
35
=
1.5441
)
[2019 CDS-II]
5.3070
5.3700
5.5635
5.6535
Validate
Solution:
We have an equilateral triangle
X
Y
Z
.
Side
X
Y
=
7
c
m
We know the area of equilateral
=
√
3
4
(
side
)
2
A
=
√
3
4
(
7
)
2
A
=
√
(
7
2
)
3
(
7
2
×
3
)
A
=
√
10.5
×
3.5
3
Now,
log
10
A
4
=
log
10
(
√
10.5
×
3.5
3
)
4
⇒
log
10
A
4
=
log
10
(
10.5
×
3.5
3
)
2
⇒
log
10
A
4
=
2
log
10
(
10.5
×
3.5
3
)
⇒
log
10
A
4
=
2
log
10
10.5
+
2
log
10
(
3.5
)
3
⇒
log
10
A
4
=
2
log
10
(
1050
100
)
+
6
log
10
(
35
10
)
⇒
log
10
A
4
=
2
log
10
1050
−
2
log
10
10
2
+
6
log
10
35
−
6
log
10
10
1
⇒
log
10
A
4
=
2
(
3.0212
)
−
4
+
6
(
1.5441
)
−
6
⇒
log
10
A
4
=
5.307
© examsnet.com
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