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Solve : log(3)x . log(4)x.log(5)x=log(3)...

Solve : `log_(3)x . log_(4)x.log_(5)x=log_(3)x.log_(4)x+log_(4)x.log_(5)+log_(5)x.log_(3)x`.

Text Solution

Verified by Experts

The correct Answer is:
60
`log_(3)x.log_(4)x.log_(5)x=log_(3)x.log_(4)x+log_(4)x.log_(5)x+log_(5)x.log_(3)x.`
Let `log_(x)3=p, log_(x)4=q, log_(x)5=4`
`rArr (1)/(pqr)=(1)/(pq)+(1)/(qr)=(1)/(pr)`
`rArr p+q+r=1`
`rArr log_(x)3+log_(x)4+log_(x)5=1`
`rArr log_(x)60=1`
`rArr x = 60`
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