# How do you simplify Log(100.0/5.7)?

Jun 16, 2017

$\log \left(\frac{100}{5.7}\right) = \textcolor{m a \ge n t a}{2 - \log \left(5.7\right)}$

#### Explanation:

(I am assuming the standard usage: $\log$ means ${\log}_{10}$)

$\log \left(\frac{a}{b}\right) = \log \left(a\right) - \log \left(b\right)$

${\log}_{10} \left(100\right) = \textcolor{b l u e}{2} \textcolor{w h i t e}{\text{XXXX}}$since ${10}^{\textcolor{b l u e}{2}} = 100$

Therefore
$\textcolor{w h i t e}{\text{XXX}} {\log}_{10} \left(\frac{100}{5.7}\right) = 2 - {\log}_{10} \left(5.7\right)$

Note that there is no simple evaluation for ${\log}_{10} \left(5.7\right)$
but if necessary you could use a calculator to determine
$\textcolor{w h i t e}{\text{XXX}} \log \left(5.7\right) \approx 0.755874856$
and from there
$\textcolor{w h i t e}{\text{XXX}} {\log}_{10} \left(\frac{100}{5.7}\right) = 2 - {\log}_{10} \left(5.7\right) \approx 1.244125144$