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9th Class Mathematics Related to Competitive Exam Question Bank Logarithms

  • question_answer
    If \[l\mathbf{og}\left( \mathbf{0}.\mathbf{37} \right)=\overline{1}.\mathbf{756}\], then the value of \[\mathbf{log37}+\mathbf{log}{{\left( \mathbf{0}.\mathbf{37} \right)}^{\mathbf{3}}}+\mathbf{log}\sqrt{0.\mathbf{37}}\]Is:

    A)  0.902                          

    B)  \[\overline{2}.146\]          

    C)  3.444   

    D)  \[\overline{1}.146\]

    Correct Answer: C

    Solution :

    (c): \[log(0.37)=\overline{1}.756\Rightarrow log37=1.756\] \[\therefore log37+log{{(0.37)}^{3}}+log\sqrt{0.37}\] \[=log37+3\,log\left( \frac{37}{100} \right)+log{{\left( \frac{37}{100} \right)}^{1/2}}\] \[=log37+3log37-3log100+\frac{1}{2}log37-\frac{1}{2}log100\] \[=\frac{9}{2}log37-\frac{7}{2}log100=\frac{9}{2}\times 1.756-\frac{7}{2}\times 2\] \[=7.902-7=0.902\]                               


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