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National and Regional Contests
Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 2
2016 Nigerian Senior MO Round 2
Problem 10
Problem 10
Part of
2016 Nigerian Senior MO Round 2
Problems
(1)
Manpulating Logarithms
Source: 2016 Nigerian Senior MO Round 2
11/16/2022
Positive numbers
x
x
x
and
y
y
y
satisfy
x
y
=
2
15
xy=2^{15}
x
y
=
2
15
and
log
2
x
⋅
log
2
y
=
60
\log_2{x} \cdot \log_2{y} = 60
lo
g
2
x
⋅
lo
g
2
y
=
60
. Find
(
log
2
x
)
3
+
(
log
2
y
)
3
3
\sqrt[3]{(\log_2{x})^3+(\log_2{y})^3}
3
(
lo
g
2
x
)
3
+
(
lo
g
2
y
)
3
logarithms
algebra