csat-suneung 2009 Q11

csat-suneung · South-Korea · csat__math-humanities 4 marks Laws of Logarithms Verify Truth of Logarithmic Statements
For a constant $a$ with $0 < a < \frac { 1 } { 2 }$, let the point where the line $y = x$ meets the curve $y = \log _ { a } x$ be $( p , p )$, and let the point where the line $y = x$ meets the curve $y = \log _ { 2 a } x$ be $( q , q )$. Which of the following statements in $\langle$Remarks$\rangle$ are correct? [4 points]
$\langle$Remarks$\rangle$ ㄱ. If $p = \frac { 1 } { 2 }$, then $a = \frac { 1 } { 4 }$. ㄴ. $p < q$ ㄷ. $a ^ { p + q } = \frac { p q } { 2 ^ { q } }$
(1) ㄱ
(2) ㄱ, ㄴ
(3) ㄱ, ㄷ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
For a constant $a$ with $0 < a < \frac { 1 } { 2 }$, let the point where the line $y = x$ meets the curve $y = \log _ { a } x$ be $( p , p )$, and let the point where the line $y = x$ meets the curve $y = \log _ { 2 a } x$ be $( q , q )$. Which of the following statements in $\langle$Remarks$\rangle$ are correct? [4 points]

$\langle$Remarks$\rangle$\\
ㄱ. If $p = \frac { 1 } { 2 }$, then $a = \frac { 1 } { 4 }$.\\
ㄴ. $p < q$\\
ㄷ. $a ^ { p + q } = \frac { p q } { 2 ^ { q } }$\\
(1) ㄱ\\
(2) ㄱ, ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ