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2
Logarithm Equation
Logarithm Equation
Source: AIME II 2013, Problem 2
April 4, 2013
logarithms
AMC
algebra
AIME
Problem Statement
Positive integers
a
a
a
and
b
b
b
satisfy the condition
log
2
(
log
2
a
(
log
2
b
(
2
1000
)
)
)
=
0.
\log_2(\log_{2^a}(\log_{2^b}(2^{1000})))=0.
lo
g
2
(
lo
g
2
a
(
lo
g
2
b
(
2
1000
)))
=
0.
Find the sum of all possible values of
a
+
b
a+b
a
+
b
.
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