Question

The mantissa of $\log 23750$ is $0.3756$. Find the value of the following.
(i) $\log 23750$
(ii) $\log 23.75$
(iii) $\log 2.375$
(iv) $\log 0.2375$
(v) $\log 23750000$
(vi) $\log 0.00002375$

Answer 1

$\log \left(2.375\right)=0.3756$

(i) $\log (2.375\times {10}^4)=4+\log \left(2.375\right)=4.3756$

(ii) $\log (2.375\times {10}^1)=1+0.3756=1.3756$

(iii) $\log \left(2.375\right)=0.3756$

(iv) $\log (2.375\times {10}^{-1})=-1+\log \left(2.375\right)=-0.6244$

(v) $\log (2.375\times {10}^7)=7+\log \left(2.375\right)=7.3756$

(vi) $\log (2.375\times {10}^{-5})=-5+\log \left(2.375\right)=-4.6244$