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3
2014 HMMT #3: Power of logarithmic expression
2014 HMMT #3: Power of logarithmic expression
Source:
February 23, 2014
HMMT
logarithms
Problem Statement
Let
A
=
1
6
(
(
log
2
(
3
)
)
3
−
(
log
2
(
6
)
)
3
−
(
log
2
(
12
)
)
3
+
(
log
2
(
24
)
)
3
)
A = \frac{1}{6}((\log_2(3))^3-(\log_2(6))^3-(\log_2(12))^3+(\log_2(24))^3)
A
=
6
1
((
lo
g
2
(
3
)
)
3
−
(
lo
g
2
(
6
)
)
3
−
(
lo
g
2
(
12
)
)
3
+
(
lo
g
2
(
24
)
)
3
)
.Compute
2
A
2^A
2
A
.
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