Question

Given that $\log \left(2\right)=0.3010$, then the number of digits in the number ${2000}^{2000}$ is :

• A. $6601$
• B. $6602$
• C. $6603$
• D. $6604$

Answer 1

The correct option is C $6603$

Let $y={2000}^{2000}$
${\log }_{10}y=2000{\log }_{10}\left(2000\right)$
$=2000({\log }_{10}2+{\log }_{10}(1000\left)\right)$
$=2000(0.3010+3)$
$=2000\left(3.3010\right)$
$=6602.$

Therefore, the number of digits will be
${\log }_{10}y+1$
$=6602+1$
$=6603$