Question

The number $N=6{\log }_{10}2+{\log }_{10}31$, lies between two successive integers, whose sum is equal to

• A. $9$
• B. $7$
• C. $11$
• D. $5$

Answer 1

The correct option is B $7$

$N=6{\log }_{10}2+{\log }_{10}31$
$\Rightarrow N={\log }_{10}64+{\log }_{10}31$
$\Rightarrow N={\log }_{10}1984{\log }_{10}1000<{\log }_{10}1984<{\log }_{10}10000\Rightarrow 3<N<4$