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8th Class Mathematics Related to Competitive Exam Question Bank Logarithms

  • question_answer
    If \[\mathbf{log2}=\mathbf{x},\,\,\mathbf{log3}=\mathbf{y}\] and \[\mathbf{log7}=\mathbf{z},\]then the value of \[\mathbf{log(8}\mathbf{.}\sqrt[\mathbf{3}]{\mathbf{21}}\mathbf{)}\]is:

    A)  \[2x+\frac{2}{3}y-\frac{1}{3}z\]          

    B)  \[2x+\frac{2}{3}y+\frac{1}{3}z\]

    C)  \[2x-\frac{2}{3}y+\frac{1}{3}z\]          

    D)  \[3x+\frac{1}{3}y+\frac{1}{3}z\]

    Correct Answer: D

    Solution :

    (d): \[log(8\sqrt[3]{21})=log8+log(\sqrt[3]{21})\] \[=log8+\log {{(21)}^{1/3}}=log({{2}^{3}})+log{{(7\times 3)}^{1/3}}\] \[=3\,log\,2+\frac{1}{3}log\,7+\frac{2}{3}log\,3=3x+\frac{1}{3}z+\frac{2}{3}y.\]


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