csat-suneung 2020 Q15

csat-suneung · South-Korea · csat__math-science 4 marks Exponential Functions Intersection and Distance between Curves

Let A be the point where the graph of the exponential function $y = a ^ { x } ( a > 1 )$ meets the line $y = \sqrt { 3 }$. For the point $\mathrm { B } ( 4,0 )$, if the line OA and the line AB are perpendicular to each other, what is the product of all values of $a$? (Here, O is the origin.) [4 points]
(1) $3 ^ { \frac { 1 } { 3 } }$
(2) $3 ^ { \frac { 2 } { 3 } }$
(3) 3
(4) $3 ^ { \frac { 4 } { 3 } }$
(5) $3 ^ { \frac { 5 } { 3 } }$

Let A be the point where the graph of the exponential function $y = a ^ { x } ( a > 1 )$ meets the line $y = \sqrt { 3 }$. For the point $\mathrm { B } ( 4,0 )$, if the line OA and the line AB are perpendicular to each other, what is the product of all values of $a$? (Here, O is the origin.) [4 points]\\
(1) $3 ^ { \frac { 1 } { 3 } }$\\
(2) $3 ^ { \frac { 2 } { 3 } }$\\
(3) 3\\
(4) $3 ^ { \frac { 4 } { 3 } }$\\
(5) $3 ^ { \frac { 5 } { 3 } }$

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