csat-suneung 2008 Q16

csat-suneung · South-Korea · csat__math-humanities 4 marks Laws of Logarithms Logarithmic Function Graph Intersection or Geometric Analysis
The line $y = 2 - x$ intersects the graphs of the two logarithmic functions $y = \log _ { 2 } x$ and $y = \log _ { 3 } x$ at points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$, respectively. Which of the following in are correct? [4 points]
ㄱ. $x _ { 1 } > y _ { 2 }$ ㄴ. $x _ { 2 } - x _ { 1 } = y _ { 1 } - y _ { 2 }$ ㄷ. $x _ { 1 } y _ { 1 } > x _ { 2 } y _ { 2 }$
(1) ㄱ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
The line $y = 2 - x$ intersects the graphs of the two logarithmic functions $y = \log _ { 2 } x$ and $y = \log _ { 3 } x$ at points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$, respectively. Which of the following in <Remarks> are correct? [4 points]

<Remarks>\\
ㄱ. $x _ { 1 } > y _ { 2 }$\\
ㄴ. $x _ { 2 } - x _ { 1 } = y _ { 1 } - y _ { 2 }$\\
ㄷ. $x _ { 1 } y _ { 1 } > x _ { 2 } y _ { 2 }$\\
(1) ㄱ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ