InterviewSolution
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InterviewSolution
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Statement-1: The solution set of the equation `"log"_(x) 2 xx "log"_(2x) 2 = "log"_(4x) 2 "is" {2^(-sqrt(2)), 2^(sqrt(2))}.` Statement-2 : `"log"_(b)a = (1)/("log"_(a)b) " and log"_(a) xy = "log"_(a) x + "log"_(a)y`A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - A We have, `"log"_(x) 2 xx "log"_(2x) 2 = "log"_(4x)2` `rArr (1)/("log"_(2)x) xx (1)/("log"_(2)2x) = (1)/("log"_(2)4x)` `rArr (1)/("log"_(2)x(1+"log"_(2)x)) = (1)/((2+"log"_(2)x))` `rArr ("log"_(2)x)^(2) = 2 rArr "log"_(2) x = +- sqrt(2) rArr x = 2^(sqrt(2)), 2^(-sqrt(2))` Hence, the solution set is `{2^(-sqrt(2)), 2^(sqrt(2))}` |
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