Question

Number of digits in the number $5^{17}$ is ...............(Use approximate value of ${\log }_{10}2$ is 0.3010)

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

Answer: (C)

$12$

Let us consider $x=5^{17}.$

Now, Taking $\log$ to the base $10$ on both the sides, we get,

$\log \left(x\right)=\log \left(5^{17}\right)=17\log \left(5\right)=17\log \left(10/2\right)=17\left[\log \right(10)-\log (2\left)\right]$

$=17(1-0.3010)=11.883$

We can now take the smallest integer not less than $11.883$, which is 12. Hence $5^{17}$ is a $12$ digit number.