Question

If $0.3<{\log }_{10}2<0.30103$, then the number of digits in $2^{100}$ is

• A. $31$
• B. $32$
• C. $33$
• D. $100$

Answer 1

Answer: (A)

$31$

Given that, $0.3<{\log }_{10}2<0.30103$
$\Rightarrow {10}^{0.3}<{10}^{{\log }_{10}2}<{10}^{0.30103}$
$\Rightarrow {10}^{0.3}<2<{10}^{0.30103}$
$\Rightarrow {10}^{30}<2^{100}<{10}^{30.103}<{10}^{31}$
Therefore, number of digits in $2^{100}$ cannot exceed $31$.
Ans: A