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If log(175)5x=log(343)7x, then the value...

If `log_(175)5x=log_(343)7x`, then the value of `log_(42)(x^(4)-2x^(2)+7)` is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Let `log_(175)5x=log_(343)7x=k`
`rArr 5x=175^(k)` and `7x=343^(k)`
`rArr (5)/(7)=((175)/(343))^(k)`
`rArr k=(1)/(2)`
Now, `5x=(175)^(1//2)`
`rArr x=sqrt(7)`
`rArr log_(42)(x^(4)-2x^(2)+7)=1`
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