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8th Class Mathematics Related to Competitive Exam Question Bank Logarithms

  • question_answer
    If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\left( {{\mathbf{x}}^{\mathbf{2}}}\mathbf{+x} \right)\mathbf{-lo}{{\mathbf{g}}_{\mathbf{5}}}\left( \mathbf{x+l} \right)\mathbf{=2}\], then the value of x is:

    A)  5                                

    B)  10

    C)  25

    D)  32

    Correct Answer: C

    Solution :

    (c): \[lo{{g}_{5}}({{x}^{2}}+x)-lo{{g}_{5}}(x+1)=2\] \[\Rightarrow lo{{g}_{5}}\left( \frac{{{x}^{2}}+x}{x+1} \right)=2\] \[\Rightarrow lo{{g}_{5}}\left[ \frac{x(x+1)}{x+1} \right]=2\] \[\Rightarrow {{\log }_{5}}x=2\Rightarrow x={{5}^{2}}=25\]               


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