# Given log4=0.6021, log9=0.9542, and log12=1.-792, how do you find log 1.2?

Jan 8, 2017

$\log 1.2 = 0.0792$

#### Explanation:

As $\log 9 = 0.9542$. we have

$\log 9 = \log {3}^{2} = 2 \log 3 = 0.9542$ i.e. $\log 3 = \frac{0.9542}{2} = 0.4771$

Hence $\log 1.2 = \log \left(\frac{4 \times 3}{10}\right) = \log 4 + \log 3 - \log 10$

= $0.6021 + 0.4771 - 1$

= $1.0792 - 1$

= $0.0792$

We could have also done

$\log 1.2 = \log \left(\frac{12}{10}\right) = \log 12 - \log 10$

= $1.0792 - 1 = 0.0792$