Question

If $0.3<{\log }_{10}2<0.30103$ then the number of digits in $2^{100}$ is

• A. $31$
• B. $33$
• C. $110$
• D. $32$

Answer 1

The correct option is A $31$

$2^{100}$

Applying log on $2^{100}$

$\therefore {\log }_{10}/2^{100})=100{\log }_{10}/2)$

$=100\times 0.3<100{\log }_{10}2<100\times 0.301$

$=30<100{\log }_{10}2<30.1$

$\therefore$ Greatest integer greater then $30.1$ is $31$

Number of digit is $31$