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9th Class Mathematics Related to Competitive Exam Question Bank Logarithms

  • question_answer
    If \[lo{{g}_{10}}5+lo{{g}_{10}}(5x+1)=log\left( x+5 \right)+1,\] then x is equal to:

    A)  1                                

    B)  3

    C)  5                                

    D)  10

    Correct Answer: B

    Solution :

    (b): \[\Leftrightarrow lo{{g}_{10}}5+lo{{g}_{10}}(5x+1)=lo{{g}_{10}}[(x+5)]+{{\log }_{10}}10\] \[\Leftrightarrow lo{{g}_{10}}5+lo{{g}_{10}}(5x+1)=lo{{g}_{10}}\left[ 10(x+5) \right]\] \[\Leftrightarrow 5(5x+1)=10(x+5)\] \[\Leftrightarrow 5x+1=2x+10\Leftrightarrow 3x=9\Leftrightarrow x=3.\]


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