Quadratic EquationHard
Question
Let (x0, y0) be solution of the following equations
(2x)ln2 = (3y)ln3
3lnx = 2lny
Then x0 is
(2x)ln2 = (3y)ln3
3lnx = 2lny
Then x0 is
Options
A.1/6
B.1/3
C.1/2
D.6
Solution
(2x)ln2 = (3y)ln3 .........(i)
3lnx = 2lny .........(ii)
⇒ (log x) (log 3) = (log y) (log 2)
⇒ log y
.........(iii)
In (i) taking log both sides
(log 2) {log 2 + log x} = log3{log 3 + log y}
(log 2)2 + (log 2) (log x) = (log 3)2 +
from (iii)
⇒ (log 2)2 - (log 3)2 =
(log x) ⇒ - log 2 = log x
⇒ x = 1/2 ⇒ x0 = 1/2
3lnx = 2lny .........(ii)
⇒ (log x) (log 3) = (log y) (log 2)
⇒ log y
.........(iii)In (i) taking log both sides
(log 2) {log 2 + log x} = log3{log 3 + log y}
(log 2)2 + (log 2) (log x) = (log 3)2 +
from (iii)⇒ (log 2)2 - (log 3)2 =
(log x) ⇒ - log 2 = log x⇒ x = 1/2 ⇒ x0 = 1/2
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