8th Class Mathematics Related to Competitive Exam Question Bank Logarithms

  • question_answer
    If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{8=x,}\]then \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \frac{\mathbf{1}}{\mathbf{80}} \right)\]is equal to:

    A)  \[-\left( 1+x \right)\] 

    B)  \[{{\left( 1+x \right)}^{-1}}\]

    C)  \[\frac{a}{10}\]                        

    D)  \[\frac{1}{10a}\]

    Correct Answer: A

    Solution :

    (a): \[\text{log}\left( \frac{1}{80} \right)=\text{lo}{{\text{g}}_{10}}1-\text{log}\,80\] \[=-\,\text{lo}{{\text{g}}_{10}}\left( 8\times 10 \right)=-({{\log }_{10}}8+{{\log }_{10}}10)=-(x+1).\]     


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