If a,b,c are distinct real number different from 1 such that
`(log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0`, then abc is equal to

Options

A. 0
B. e
C. 1
D. none of these

Explanation

`(log_(b)alog_(c)a-1) + (log_(a)b.log_(c)b-1)+(log_(a)clog_(b)c-1)=0`
`rArr (loga)/(logb).(loga)/(logc) +(logb)/(loga). (log b)/(log c) + (log c)/(log a).(log c)/(log b) =3`
`rArr (loga+logb+logc)=0 [therefore "if" a^(3)+b^(3)+c^(3)-3abc=0`, then a+b+c=0 if `a ne b ne c`
`rArr logabc = log1 rArr abc=1`