For relation `2 log y - log x - log ( y-1)`=0

Options

A. domain `=(4,+oo),"range"=(1+oo)`
B. domain`=(4,oo),"range"=(2+oo)`
C. domain`=(2,oo),"range"=(2,+oo)`
D. none of these

Answer

A

Explanation

Here , `log.(y^(2))/(x(y-1))=0`
`or" "(y^(2))/(x(y-1))=1`
`"or "y^(2)=xy-x`
`"or "y^(2)-xy+x=0`
`therefore" "y=(xpnsqrt(x^(2)-4x))/(2)`
So y is real if
`x^(2)-4xge0`
`"or "x(x-4)ge0`
`therefore" "xle0orxge4.`
But `xgt0` for log x to be defined.
`"So, "xge4`
`"Now, "x=(y^(2))/(y-1)ge4`
`"or "(y^(2)-4y+4)/(y-1)ge0`
`"or "(y-2)^(2)//(y-1)ge0`
`rArr" "yge1`
But `ygt1` for log `(y-1)` to be real.