2log18+3log24-6log6=log-------
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Answered by
1
How do you simplify
2
log
3
+
log
4
−
log
6
?
Precalculus Common Logs
1 Answer
mason m
Feb 13, 2016
log
(
6
)
Explanation:
First, simplify
2
log
(
3
)
through the rule:
b
⋅
log
(
a
)
=
log
(
a
b
)
Thus,
2
log
(
3
)
=
log
(
3
2
)
=
log
(
9
)
.
Substitute this back into the original expression:
=
log
(
9
)
+
log
(
4
)
−
log
(
6
)
We can now use the following rule regarding the addition of logarithms (with the same base, which we do have in this scenario):
log
(
a
)
+
log
(
b
)
=
log
(
a
b
)
Thus the first two logarithms can be combined as follows:
log
(
9
)
+
log
(
4
)
=
log
(
9
⋅
4
)
=
log
(
36
)
Substituting this back into the expression, we obtain:
=
log
(
36
)
−
log
(
6
)
Now, to subtract logarithms with the same base, we use the rule:
log
(
a
)
−
log
(
b
)
=
log
(
a
b
)
Thus, the expression becomes
=
log
(
36
6
)
=
log
(
6
)
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