The product of all the real solution(s) of the equation 2 loggix-1)=2+log(x-1) 3-log(x-1) is
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Answer:
∣x−1∣
log
3
x
2
−2log
x
9
=(x−1)
7
L.H.S of the above equation exist when x
=1
and x cannot be less than 1
Taking logarithm on both sides, we get
(log
3
x
2
−2log
x
9)log(x−1)=7log(x−1)[∵loga
m
=mloga]
⇒(2log
3
x−
log
3
x
4
)log(x−1)=7log(x−1)[∵log
a
b=
log
b
a
1
]
⇒(2log
3
x−
log
3
x
4
)log(x−1)=7log(x−1)
⇒log(x−1)=0 ⇒x=2
And 2(log
3
x)
2
−7log
3
x−4=0
⇒log
3
x=4,
2
−1
⇒x=81,
3
1
Since, x>1
Therefore, x=2,81
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