8th Class Mathematics Logarithms 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 \[={{\log }_{xyz}}(xy)+{{\log }_{xyz}}(yz)+{{\log }_{xyz}}(zx)\] \[={{\log }_{xyz}}\left( xy\times yz\times zx \right)={{\log }_{xyz}}{{\left( xyz \right)}^{2}}\] \[=2\,\text{lo}{{\text{g}}_{xyz}}(xyz)=2\times 1=2.\]

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