8th Class Mathematics Logarithms Question Bank Logarithms

  • question_answer If \[\mathbf{log}\left( \mathbf{0}\mathbf{.37} \right)\mathbf{=}\overline{\mathbf{1}}\mathbf{.756,}\]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)  \[\overline{1}.1\text{ }46\]

    Correct Answer: C

    Solution :

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

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