Question

If `sqrt((log)_2x)-0. 5=(log)_2sqrt(x ,)` then `x` equals odd integer (b) prime number composite number (d) irrational
A. odd integer
B. prime number
C. composite number
D. irrational

Answer 1

Correct Answer - B
`sqrt(log_(2)x)-0.5 = log_(2) sqrtx`
` or sqrt(log_(2)x)-0.5 = 0.5 log_(2)x`
` rArr y - 0.5 = 0.5y^(2)`
`rArr y^(2) - 2y + 1 = 0`
` rArr y = 1`
`rArr log_(2) x = 1`
` rArr x = 2`