Question

Write the characteristic of each of the following
(i) $\log 4576$
(ii) $\log 24.56$
(iii) $\log 0.00257$
(iv) $\log 0.0756$
(v) $\log 0.2798$
(vi) $\log 6.453$

Answer 1

(i) $\log \left(4576\right)=\log ({10}^3\times 4.576)$

$=3+{\log }_{10}4.576\Rightarrow$ Characteristic $=3$

(ii) $\log \left(24.56\right)=\log (10\times 2.456)=1+\log \left(2.456\right)\Rightarrow$ Characteristic $=1$

(iii) $\log (2.57\times {10}^{-3})=-3+\log \left(2.57\right)\Rightarrow$ Characteristic $=-3$

(iv) $\log \left(0.0756\right)=\log (7.56\times {10}^{-2})$

$=-2+\log \left(7.56\right)\Rightarrow$ Characteristic $=-2$

(v) $\log (2.798\times {10}^{-1})=-1+\log \left(2.798\right)\Rightarrow$ Characteristic $=-1$

(vi) $\log \left(6.453\right)=0+\log \left(6.453\right)\Rightarrow$ Characteristic $=0$