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If log(a)b+log(b)c+log(c)a vanishes wher...

If `log_(a)b+log_(b)c+log_(c)a` vanishes where a, b and c are positive reals different than unity then the value of `(log_(a)b)^(3) + (log_(b)c)^(3) + (log_(c)a)^(3)` is

A

an odd prime

B

an even prime

C

an odd composite

D

an irrational number

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The correct Answer is:
A
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