Question

Write the characteristic of the following.
(i) $\log 27.91$
(ii) $\log 0.02871$
(iii) $\log 0.000987$
(iv) $\log 2475$

Answer 1

(i) ${\log }_{10}(10\times 2.791)={\log }_{10}10+{\log }_{10}\left(2.791\right)$

$=1+{\log }_{10}\left(2.791\right)\Rightarrow$ Characteristic $=1$

(ii) ${\log }_{10}(2.871\times {10}^{-2})=-2+{\log }_{10}\left(2.871\right)\Rightarrow$ Characteristic $=-2$

(iii) ${\log }_{10}(9.87\times {10}^{-4})=-4+{\log }_{10}\left(9.87\right)\Rightarrow$ Characteristic $=-4$

(iv) $\log \left(2475\right)=\log (2.475\times {10}^3)$

$={\log }_{10}{10}^3+{\log }_{10}2.475=3+{\log }_{10}2.475\Rightarrow$ Characteristic $=+3$