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The set of real values of x satisfying t...

The set of real values of `x` satisfying the equation `|x-1|^(log_3(x^2)-2log_x(9))=(x-1)^7`

A

`1/sqrt3`

B

1

C

2

D

81

Text Solution

Verified by Experts

The correct Answer is:
C, D
`|x-1|^(log_(3)x^(2)-2log_(x)9*)= (x-1)^(7)`
Since L.H.S. ` gt 0." So, "x gt 1`
` :. (x-1)^(log_(3)x^(2)-2 log_(x)9)=(x-1)^(7)`
`rArr x - 1 = 1 or log_(3)x^(2) - 2log_(x)9=7`
` rArr x = 2 or 2 log_(3) x - 4 1/(log_(3)x) - 7 = 0`
` rArr x = 2 or 2(log_(3)x)^(2) - 7 log_(3)x-4 = 0`
` rArr x = 2 or log _(3) x =- 1//2, 4`
` rArr x = 2 or x = 3^(-1//2) , 3^(4)`
` rArr x = 2, 81`
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