Question

If ${\log }_{10}2=0.3010$, then the number of digits in $2^{64}$ is

• A. $18$
• B. $24$
• C. $22$
• D. $20$

Answer 1

The correct option is D $20$

Given ${\log }_{10}2=0.301$

${\log }_{10}{2}^{64}=64\times {\log }_{10}2=64\times 0.3010=19.264$

$\Rightarrow 2^{64}={10}^{19.264}$

The number of digits in ${10}^{19}$ is $20$ , there will be $21$ digits from ${10}^{21}$

The number ${10}^{19.264}$ lies between them

Therefore the number of digits in ${10}^{19.264}$ is $20$

Therefore the correct option is $D$