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UPSC CDS Math Logarithm Questions
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© examsnet.com
Question : 12
Total: 16
What is the solution of the equation
x
log
10
10
3
+
log
10
3
=
log
10
(
2
+
3
x
)
+
x
?
[2017 CDS-I]
10
3
1
0
Validate
Solution:
x
log
10
(
10
3
)
+
log
10
3
=
log
10
(
2
+
3
x
)
+
x
⇒
x
[
log
10
(
10
3
)
−
1
]
+
log
10
3
=
log
10
(
2
+
3
x
)
⇒
x
[
log
10
(
10
3
)
−
log
10
10
]
+
log
10
3
=
log
10
(
2
+
3
x
)
⇒
x
log
10
[
(
10
3
)
10
]
+
log
10
3
=
log
10
(
2
+
3
x
)
⇒
x
log
10
(
1
3
)
+
log
10
3
=
log
10
(
2
+
3
x
)
⇒
log
10
(
1
3
x
)
+
log
10
3
=
log
10
(
2
+
3
x
)
⇒
log
10
(
3
3
x
)
=
log
10
(
2
+
3
x
)
⇒
3
3
x
=
2
+
3
x
For
x
=
0
,
LHS
=
3
3
x
=
3
3
0
=
3
1
=
3
RHS
=
2
+
3
x
=
2
+
3
0
=
2
+
1
=
3
>Thus, the solution of the given equation is x = 0.
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