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JEE Main & Advanced Sample Paper JEE Main Sample Paper-14

  • question_answer
    The value of \[\left( \frac{1}{{{\log }_{1/3}}\frac{1}{5}}+\frac{1}{{{\log }_{1/4}}\frac{1}{5}} \right)\] lies in the interval

    A)  (0, 1)                                    

    B)  (1, 2)            

    C)  (2, 3)                                    

    D)  (- 1, 0)

    Correct Answer: B

    Solution :

     \[\frac{1}{{{\log }_{1/3}}\frac{1}{5}}+\frac{1}{{{\log }_{1/4}}\frac{1}{5}}\] \[={{\log }_{1/5}}\frac{1}{3}+{{\log }_{1/5}}\frac{1}{4}\] \[={{\log }_{5}}3+{{\log }_{5}}4={{\log }_{5}}12\] \[\because \]     \[5<12<{{5}^{2}}\] So,          \[{{\log }_{5}}\,12\,\in \,(1,2)\]


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