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1984 IMO Shortlist
20
Solve the logarithmic inequality (ISL84)
Solve the logarithmic inequality (ISL84)
Source:
September 8, 2010
inequalities
logarithms
algebra
IMO Shortlist
Problem Statement
Determine all pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of positive real numbers with
a
≠
1
a \neq 1
a
=
1
such that
log
a
b
<
log
a
+
1
(
b
+
1
)
.
\log_a b < \log_{a+1} (b + 1).
lo
g
a
b
<
lo
g
a
+
1
(
b
+
1
)
.
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