InterviewSolution
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InterviewSolution
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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 |
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Answer» `(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` |
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