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8th Class Mathematics Related to Competitive Exam Question Bank Logarithms

  • question_answer
    The value of \[\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{4} \right)\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{4}}}\mathbf{5} \right)\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{6} \right)\]\[\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{6}}}\mathbf{7} \right)\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{7}}}\mathbf{8} \right)\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{8}}}\mathbf{9} \right)\]is:

    A)  2                                

    B)  7             

    C)  8

    D)  33

    Correct Answer: C

    Solution :

    (a): Given expression=\[\left( \frac{\log 4}{\log 3}\times \frac{\log 5}{\log 4}\times \frac{\log 6}{\log 5}\times \frac{\log 7}{\log 6}\times \frac{\log 8}{\log 7}\times \frac{\log 9}{\log 8} \right)\] \[=\frac{\log 9}{\log 3}=\frac{\log {{3}^{2}}}{\log 3}=\frac{2\log 3}{\log 3}=2.\]                      


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