prove that log12/15+2log6/8+1/3log8/27=log3/10
Answers
Answered by
0
Answer:
If
a
,
b
>
0
then:
log
a
b
=
log
a
+
log
b
and
log
(
a
b
)
=
log
a
−
log
b
Hence:
log
a
n
=
n
log
a
for any integer
n
>
0
So we find:
1
2
log
9
+
2
log
6
+
1
4
log
81
−
log
12
=
1
2
log
3
2
+
1
4
log
3
4
+
log
6
2
−
log
12
=
1
2
(
2
log
3
)
+
1
4
(
4
log
3
)
+
log
(
36
12
)
=
log
3
+
log
3
+
log
3
=
3
log
3
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