Question

Given, ${\log }_{10}2=0.3010,{\log }_{10}3=0.4771$. Find the number of digits in $5^{200}$

• A. $140$
• B. $47$
• C. $12$
• D. none of these

Answer 1

The correct option is A $140$

Let $y=5^{200}$

$\Rightarrow {\log }_{10}y=200{\log }_{10}5\Rightarrow {\log }_{10}y=200{\log }_{10}\frac{10}{2}\Rightarrow {\log }_{10}y=200{\log }_{10}10-200{\log }_{10}2.................[\because \log \frac{a}{b}=\log a-\log b]\Rightarrow {\log }_{10}y=200(1-0.3010)=200\left(0.699\right)\Rightarrow {\log }_{10}y=139.8$

Hence number of digits in $5^{200}$ is $140$