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2005 AIME Problems
5
Ordered Pairs and Logarithms
Ordered Pairs and Logarithms
Source:
November 13, 2005
logarithms
floor function
Problem Statement
Determine the number of ordered pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of integers such that
log
a
b
+
6
log
b
a
=
5
\log_a b + 6\log_b a=5
lo
g
a
b
+
6
lo
g
b
a
=
5
,
2
≤
a
≤
2005
2 \leq a \leq 2005
2
≤
a
≤
2005
, and
2
≤
b
≤
2005
2 \leq b \leq 2005
2
≤
b
≤
2005
.
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