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Byju's Answer
Standard XII
Mathematics
Combination
Find the real...
Question
Find the real solution to the logarithmic equation
ln
(
x
)
+
ln
(
2
)
=
3
A
no real solutions
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B
0.5
×
e
3
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C
e
3
/
ln
(
2
)
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D
3
e
/
2
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E
3
ln
(
2
)
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Solution
The correct option is
B
0.5
×
e
3
Let both sides be exponents of the base
e
.
The equation
ln
(
x
)
+
ln
(
2
)
=
3
⇒
e
ln
(
x
)
+
ln
(
2
)
=
e
3
⇒
e
ln
(
2
x
)
=
e
3
By now you should know that when the base of the exponent and the base of the logarithm are the same, the left side can be written
x
.
The equation
e
ln
(
2
x
)
=
e
3
⇒
2
x
=
e
3
⟹
x
=
0.5
×
e
3
Hence, option B is correct.
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