csat-suneung 2005 Q5

csat-suneung · South-Korea · csat__math-humanities 3 marks Laws of Logarithms Verify Truth of Logarithmic Statements
From the following , select all correct statements. [3 points]
ㄱ. $2 ^ { \log _ { 2 } 1 + \log _ { 2 } 2 + \log _ { 2 } 3 + \cdots + \log _ { 2 } 10 } = 10$ ㄴ. $\log _ { 2 } \left( 2 ^ { 1 } \times 2 ^ { 2 } \times 2 ^ { 3 } \times \cdots \times 2 ^ { 10 } \right) ^ { 2 } = 55 ^ { 2 }$ ㄷ. $\left( \log _ { 2 } 2 ^ { 1 } \right) \left( \log _ { 2 } 2 ^ { 2 } \right) \left( \log _ { 2 } 2 ^ { 3 } \right) \cdots \left( \log _ { 2 } 2 ^ { 10 } \right) = 55$
(1) ㄱ
(2) ㄴ
(3) ㄷ
(4) ㄱ, ㄷ
(5) ㄱ, ㄴ, ㄷ
From the following <Remarks>, select all correct statements. [3 points]

<Remarks>\\
ㄱ. $2 ^ { \log _ { 2 } 1 + \log _ { 2 } 2 + \log _ { 2 } 3 + \cdots + \log _ { 2 } 10 } = 10$\\
ㄴ. $\log _ { 2 } \left( 2 ^ { 1 } \times 2 ^ { 2 } \times 2 ^ { 3 } \times \cdots \times 2 ^ { 10 } \right) ^ { 2 } = 55 ^ { 2 }$\\
ㄷ. $\left( \log _ { 2 } 2 ^ { 1 } \right) \left( \log _ { 2 } 2 ^ { 2 } \right) \left( \log _ { 2 } 2 ^ { 3 } \right) \cdots \left( \log _ { 2 } 2 ^ { 10 } \right) = 55$\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄷ\\
(4) ㄱ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ