InterviewSolution
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InterviewSolution
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If `x^({(3)/(4)("log"_(3)x)^(2) + ("log"_(3)x)-(5)/(4)}) = sqrt(3)`, then x hasA. all integral valuesB. two integral values and one irrational valuesC. all irrational valuesD. two rational values and an irrational value |
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Answer» Correct Answer - D We have, `x^({(3)/(4)("log"_(3)x)^(2) + ("log"_(3)x)-(5)/(4)}) = sqrt(3)` `rArr (3)/(4) ("log"_(3) x)^(2) + ("log"_(3) x)- (5)/(4) = "log"_(x) sqrt(3)` `rArr (3)/(4) ("log"_(3)x)^(2) + "log"_(3) x - (5)/(4) = (1)/(2"log"_(3)x)` `rArr (3)/(2) ("log"_(3)x)^(3) + 2("log"_(3)x)^(2)- (5)/(2)("log"_(3)x)-1 = 0` `rArr 3("log"_(3)x)^(3) + 4("log"_(3)x)^(2) -5("log"_(3)x) -2 =0` `rArr ("log"_(3)x-1)(3"log"_(3)x+1)("log"_(3)x+2) =0` `rArr "log"_(3)x =1, -(1)/(3), -2 rArr x = 3, 3^(-1//3), 3^(-2)` Clearly, x takes two rational values and an irrational value. |
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