Question

Number of digits in $4^{16}\cdot 5^{25}$ is equal to (Given ${\log }_{10}2=0.3010$ )

• A. 27
• B. 28
• C. 29
• D. 30

Answer 1

Answer: (B)

Let $N=2^{32}\cdot 5^{25}=2^7(2\cdot 5{)}^{25}=128\cdot 10^{25}$
$\Rightarrow {\log }_{10}N=25+7{\log }_{10^2}2=25+7\times 0.3010=25+2.107=27.107$
$\Rightarrow N\text{ is a }28\text{ digit number. }$