Question

If ${\log }_{10}2=0\cdot 3010,{\log }_{10}3=0\cdot 4771$, then the number of digits in $5^{200}$ are

• A. $120$
• B. $145$
• C. $160$
• D. none of these

Answer 1

The correct option is D none of these

Let $N=5^{200}$
$\Rightarrow \log N=200\log \left(5\right)=200(1-\log 2)$, base of the logarithm is 10.
$\Rightarrow \log N=200(1-0.301)=139.8$
Hence, number of digits in $N$ is $140$.