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Mathematics
Problem
If
log
a
b
+
log
b
c
+
log
c
a
\log_a b + \log_b c + \log_c a
lo
g
a
b
+
lo
g
b
c
+
lo
g
c
a
vanishes where
a
a
a
,
b
b
b
and
c
c
c
are positive reals different than unity then the value of
(
log
a
b
)
3
+
(
log
b
c
)
3
+
(
log
c
a
)
3
(\log_a b)^3 + (\log_b c)^3 + (\log_c a)^3
(
lo
g
a
b
)
3
+
(
lo
g
b
c
)
3
+
(
lo
g
c
a
)
3
is (a) an odd prime (b) an even prime (c) an odd composite (d) an irrational number
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