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2019 Malaysia National Olympiad
1
Sum of logarithms
Sum of logarithms
Source: Malaysia National Math Olympiad - Sulong Problem 1
October 26, 2019
logarithms
algebra
Problem Statement
Evaluate the following sum
1
log
2
1
7
+
1
log
3
1
7
+
1
log
4
1
7
+
1
log
5
1
7
+
1
log
6
1
7
−
1
log
7
1
7
−
1
log
8
1
7
−
1
log
9
1
7
−
1
log
10
1
7
\frac{1}{\log_2{\frac{1}{7}}}+\frac{1}{\log_3{\frac{1}{7}}}+\frac{1}{\log_4{\frac{1}{7}}}+\frac{1}{\log_5{\frac{1}{7}}}+\frac{1}{\log_6{\frac{1}{7}}}-\frac{1}{\log_7{\frac{1}{7}}}-\frac{1}{\log_8{\frac{1}{7}}}-\frac{1}{\log_9{\frac{1}{7}}}-\frac{1}{\log_{10}{\frac{1}{7}}}
lo
g
2
7
1
1
+
lo
g
3
7
1
1
+
lo
g
4
7
1
1
+
lo
g
5
7
1
1
+
lo
g
6
7
1
1
−
lo
g
7
7
1
1
−
lo
g
8
7
1
1
−
lo
g
9
7
1
1
−
lo
g
10
7
1
1
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