Question

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

Answer 1

Correct Answer - 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`