9th Class Mathematics Related to Competitive Exam Question Bank Logarithms

  • question_answer
    Simplify: \[\left[ \frac{1}{{{\log }_{xy}}(xyz)}+\frac{1}{{{\log }_{yz}}(xyz)}+\frac{1}{{{\log }_{zx}}(xyz)} \right]\]  

    A)  1                                

    B)  2

    C)  3                                

    D)  0

    Correct Answer: B

    Solution :

    (b): Given expression \[=lo{{g}_{xyz}}(xy)+lo{{g}_{xyz}}\left( yz \right)+lo{{g}_{xyz}}(zx)\] \[=lo{{g}_{xyz}}(xy\times yz\times zx)=lo{{g}_{xyz}}{{(xyz)}^{2}}\] \[=21o{{g}_{xyz}}\left( xyz \right)=2\times 1=2.\]


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