Question

Find the value of $\log \left(100/90\right)$

Answer 1

Find the value

${\log }_{10}\left(100/90\right)$

$=\log \left(\frac{10}{9}\right)$

$=\log \left(10\right)-\log \left(9\right)$ $\left(\because log\left(\frac{a}{b}\right)=log\left(a\right)-log\left(b\right)\right)$

$=\log \left(10\right)-\log {\left(3\right)}^2$

$=1-2\log \left(3\right)$ $\left(\because log\left(a^b\right)=blog\left(a\right)\right)$

Hence, the value of $\log \left(100/90\right)$ is .$1-2\log \left(3\right)$.