prove that 1/log3 6+ 1/log9 =3
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Answer:
Given,
1,log
9
(3
1−x
+2),log
3
[4.3
x
−1]areinA.p
⇒2log
9
(3
1−x
+2)=1+log
3
[4.3
x
−1]
⇒log
3
(3
1−x
+2)=log
3
3
+log
3
[4.3
x
−1]
=log
3
(3(4.3
x
−1))
=3
1−x
+2=3(4.3
x
−1)
=3
−x
+
3
2
=4.3
x
−1
3
x
1
+
3
2
+1=4.3
x
3
x
1
+
3
5
=4.3
x
Let 3
x
=t
t
1
+
3
5
=4t
12t
2
−5t−3=0
(4t−3)(3t+1)=0
t=
4
3
OR t
=
3
−1
3
x
=
4
3
4x=
log3
log3−log4
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