11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer The value of \[x\] satisfying\[{{\log }_{a}}x+{{\log }_{\sqrt{a}}}x+{{\log }_{3\sqrt{a}}}x+.........{{\log }_{a\sqrt{a}}}x=\frac{a+1}{2}\] will be

    A) \[x=a\]

    B) \[x={{a}^{a}}\]

    C) \[x={{a}^{-1/a}}\]

    D) \[x={{a}^{1/a}}\]

    Correct Answer: D

    Solution :

    \[{{\log }_{a}}x+2{{\log }_{a}}x+.......+a{{\log }_{a}}x=\frac{a+1}{2}\] \[\Rightarrow \] \[{{\log }_{a}}x(1+2+........+a)=\frac{a+1}{2}\] \[\Rightarrow \]  \[{{\log }_{a}}x.\frac{a(a+1)}{2}=\frac{a+1}{2}\]\[\Rightarrow \]\[({{10}^{12}}+{{10}^{11}}+......+1)\].


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