# Value of log(0.02)/(0.07)?

Jun 15, 2018

Well, is it $\log \setminus \frac{\left(0.02\right)}{\left(0.07\right)}$ or $\log \frac{0.02}{0.07}$? Use your calculator.

$\textcolor{b l u e}{\log \setminus \frac{\left(0.02\right)}{\left(0.07\right)}} = \log \left(\frac{2}{7}\right) = \log 2 - \log 7$

$= 0.3010 - 0.8451 = \textcolor{b l u e}{- 0.5441 \ldots}$

$\textcolor{b l u e}{\log \frac{0.02}{0.07}} = \frac{\log \left(2 \cdot {10}^{- 2}\right)}{7 \cdot {10}^{- 2}}$

$= \frac{\log 2 - 2 \log 10}{7 \cdot {10}^{- 2}}$

$= \frac{100 \log 2 - 200 \log 10}{7}$

$= \frac{30.10 - 200}{7}$

$= \frac{28}{7} + \frac{2.10}{7} - \frac{210}{7} + \frac{10}{7}$

$= 4.00 + 0.30 - 30.00 + 1.42857$

$= \textcolor{b l u e}{- 24.27}$