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9th Class Mathematics Related to Competitive Exam Question Bank Logarithms

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

    A)  2  

    B)  7

    C)  8                    

    D)  33

    Correct Answer: A

    Solution :

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


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