# How do you evaluate log0.003?

Dec 18, 2016

$\overline{3} .4771$ or $- 2.5229$

#### Explanation:

$\log 0.003$

= $\log \left(\frac{3}{1000}\right)$

= $\log 3 - \log 1000$

= $\log 3 - \log {10}^{3}$

= $\log 3 - 3 \log 10$

= $0.4771 - 3$

= $\overline{3} .4771$ or $- 2.5229$

Note that in $\overline{3} .4771$ while characteristic $3$ is negative, mantissa is positive and is $0.4771$