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1978 IMO Longlists
37
Simplifying a logarithmic expression
Simplifying a logarithmic expression
Source:
October 30, 2010
logarithms
algebra proposed
algebra
Problem Statement
Simplify
1
log
a
(
a
b
c
)
+
1
log
b
(
a
b
c
)
+
1
log
c
(
a
b
c
)
,
\frac{1}{\log_a(abc)}+\frac{1}{\log_b(abc)}+\frac{1}{\log_c(abc)},
lo
g
a
(
ab
c
)
1
+
lo
g
b
(
ab
c
)
1
+
lo
g
c
(
ab
c
)
1
,
where
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive real numbers.
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