Number of real values of `x` satisfying the equation `(log)_2(x^2-x)(log)_2((x-1)/x)+((log)_2x)^2=4,i s` 0 (b) 2 (c) 3 (d) 7

Options

A. 0
B. 2
C. 3
D. 7

Answer

B

Explanation

We have ` log_(2) (x^(2) - x) log_(2) ((x-1)/x) + (log_(2) x) ^(2) = 4`
` rArr [log(x-1)+log x][log(x-1)-log x] + (log_(2)x)^(2) = 4`
`rArr [log_(2)(x-1)]^(2)-(log_(2)x)^(2) + (log_(2)x)^(2) - 4 = 0`
` rArr [log_(2)(x-1)]^(2) = 4`
` rArr log_(2)(x-1) = pm 2`
`rArr x - 1 = 4 or 1/4`
` rArr x = 5 or 5/4`