• # 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)  $\overline{1}.1\text{ }46$

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