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2
2021 Algebra/NT #2: raised to the log power
2021 Algebra/NT #2: raised to the log power
Source:
May 30, 2021
algebra
Problem Statement
Compute the number of ordered pairs of integers
(
a
,
b
)
,
(a, b),
(
a
,
b
)
,
with
2
≤
a
,
b
≤
2021
,
2 \le a, b \le 2021,
2
≤
a
,
b
≤
2021
,
that satisfy the equation
a
log
b
(
a
−
4
)
=
b
log
a
(
b
a
−
3
)
.
a^{\log_b \left(a^{-4}\right)} = b^{\log_a \left(ba^{-3}\right)}.
a
l
o
g
b
(
a
−
4
)
=
b
l
o
g
a
(
b
a
−
3
)
.
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