Question

If ${\log }_{10}2=0.3010$, then the number of digits in ${256}^{50}$ are

• A. $120$
• B. $121$
• C. $256$
• D. $50$

Answer 1

The correct option is B $121$

Let $x={256}^{50}$
By taking log on both the sides
$\log x=50{\log }_{10}256$
$\Rightarrow \log x=50{\log }_{10}{2}^8$
$=400{\log }_{10}2=400\times \left(0.3010\right)$
$\log x=120.4$
number of digits in ${256}^{50}$ is $120+1=121$