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JEE Main & Advanced Mathematics Equations and Inequalities Question Bank Self Evaluation Test - Linear Inequalities

  • question_answer
    Solution set of the inequality \[{{\log }_{3}}(x+2)(x+4)+lo{{g}_{1/3}}(x+2)<\frac{1}{2}\log \sqrt{3}\,\,7\,(1)\]  is

    A) \[(-2,-1)\]

    B) \[(-2,3)\]

    C) \[(-1,3)\]

    D) \[(3,\infty )\]

    Correct Answer: B

    Solution :

    [b] \[(x+2)(x+4)>0.x+2>0\Rightarrow x>-2.\] Now (1) can be written as \[{{\log }_{3}}(x+2)(x+4)-lo{{g}_{3}}(x+2)<\frac{(log7)/2}{(log3)/2}\] \[\Rightarrow {{\log }_{3}}(x+4)<lo{{g}_{3}}^{7}\Rightarrow x+4<7\,\,or\,\,x<3.\]


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