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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

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

log_(a)b = log_(b)c = log_(c)a, then a, b and c are such that

a^(log_(b)c)=c^(log_(b)a)

Find the values : (log_(a)b)xx(log_(b)c)xx(log_(c )d)xx(log_(d)a)

the value of a^(log((b)/(c)))*b^(log((c)/(a)))c^(log((a)/(b)))

Prove that log_(b^3)a xx log_(c^3)b xx log_(a^3)c = 1/27

log_(a)a*log_(c)a+log_(c)b*log_(a)b+log_(a)c*log_(b)c=3 (where a,b,c are different positive real nu then find the value of abc.